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## Field Theory (field + theory)
Kinds of Field Theory
## Selected Abstracts## Generality with specificity: the dynamic field theory generalizes across tasks and time scales DEVELOPMENTAL SCIENCE, Issue 4 2008Vanessa R. SimmeringA central goal in cognitive and developmental science is to develop models of behavior that can generalize across both tasks and development while maintaining a commitment to detailed behavioral prediction. This paper presents tests of one such model, the Dynamic Field Theory (DFT). The DFT was originally proposed to capture delay-dependent biases in spatial recall and developmental changes in spatial recall performance. More recently, the theory was generalized to adults' performance in a second spatial working memory task, position discrimination. Here we use the theory to predict a specific, complex developmental pattern in position discrimination. Data with 3- to 6-year-old children and adults confirm these predictions, demonstrating that the DFT achieves generality across tasks and time scales, as well as the specificity necessary to generate novel, falsifiable predictions. [source] ## Numerical Self-Consistent Field Theory of Cylindrical Polyelectrolyte Brushes MACROMOLECULAR THEORY AND SIMULATIONS, Issue 3 2009Li-Jian QuAbstract A single cylindrical polyelectrolyte brush is studied by self-consistent field (SCF) theory and the results compared with predictions from scaling theory. It is shown that the SCF theory results give the general trends as well as insight into the crossover regions between different regimes. The density profiles of the polyions and small ions indicate that the systems are locally electroneutral. The salted brush bears characteristics similar to those of a neutral brush. Counter-intuitively, the chains are not uniformly stretched in the osmotic regime. The free-end monomers shift to the outer region and an exclusion zone appears and grows with decreasing of salt concentration. [source] ## Morphology of ABCD Tetrablock Copolymers Predicted by Self-Consistent Field Theory MACROMOLECULAR THEORY AND SIMULATIONS, Issue 4 2005Rong WangAbstract Summary: We studied the two-dimensional (2D) microphase-separated morphology of linear ABCD tetrablock copolymers by self-consistent field theory. By varying the interaction parameters and the compositions, we found at least twelve structures, two of which , "four-color" lamellae and "three-color" core-shell hexagonal phase , prove the existing experimental observations. These morphologies were discussed in correlation with the volume fraction of the components and the interaction parameters. A specific behavior of symmetrical tetrablock copolymers, i.e., fA,=,fD and fB,=,fC, is that the stable phases are lamellae, which is different from symmetrical ABC triblock copolymer having order-to-order transition. These results are helpful for the design of new block copolymer-based nanomaterials. [source] ## Almost-anywhere theories: Reductionism and universality of emergence COMPLEXITY, Issue 6 2010Ignazio LicataAbstract Here, we aim to show that reductionism and emergence play a complementary role in understanding natural processes and in the dynamics of science explanation. In particular, we will show that the renormalization group,one of the most refined tools of Theoretical Physics,allows to understand the importance of emergent processes' role in Nature identifying them as universal organization processes, that is, they are scale independent. We can use the syntaxes of Quantum Field Theory and the processes of Spontaneous Symmetry Breaking as a trans-disciplinary theoretical scenario for many other forms of complexity, especially the biological and cognitive ones. © 2010 Wiley Periodicals, Inc. Complexity, 2010 [source] ## Quantitative Phase Field Modeling of Precipitation Processes, ADVANCED ENGINEERING MATERIALS, Issue 12 2006Q. BronchardPhase Field modelling of microstructural evolution in alloys has already a long and successful history. One of the basics of the theory is the introduction of continuous fields (concentration, long-range order parameters) that describe the local state of the alloy. These fields have a meaning only at a mesoscopic scale. One consequence is that we can treat much larger systems than with microscopic methods such as Monte Carlo or molecular dynamics simulations. The aim of this work is to precisely analyse the status of the mesoscopic free energy densities that are used in Phase Field theories and, simultaneously, to clarify the form that the Phase Field equations should adopt. [source] ## Field theory for biogeography: a spatially explicit model for predicting patterns of biodiversity ECOLOGY LETTERS, Issue 1 2010James P. O'DwyerAbstract Predicting the variation of biodiversity across the surface of the Earth is a fundamental issue in ecology, and in this article we focus on one of the most widely studied spatial biodiversity patterns: the species,area relationship (SAR). The SAR is a central tool in conservation, being used to predict species loss following global climate change, and is striking in its universality throughout different geographical regions and across the tree of life. In this article we draw upon the methods of quantum field theory and the foundation of neutral community ecology to derive the first spatially explicit neutral prediction for the SAR. We find that the SAR has three phases, with a power law increase at intermediate scales, consistent with decades of documented empirical patterns. Our model also provides a building block for incorporating non-neutral biological variation, with the potential to bridge the gap between neutral and niche-based approaches to community assembly. Ecology Letters (2010) 13: 87,95 [source] ## Field theory on nonanticommutative superspace FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2008M. DimitrijeviAbstract We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on a special choice of a twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to a deformed Leibniz rule for SUSY transformations. Superfields are multiplied by using a ,-product which is noncommutative, hermitian and finite when expanded in power series of the deformation parameter. One possible deformation of the Wess-Zumino action is proposed and analysed in detail. Differently from most of the literature concerning this subject, we work in Minkowski space-time. [source] ## Field theory on a non-commutative plane: a non-perturbative study FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5 2004F. HofheinzAbstract The 2d gauge theory on the lattice is equivalent to the twisted Eguchi,Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non-commutative gauge theory, so the observed large N scaling demonstrates the non-perturbative renormalizability of this non-commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter. Next we investigate the 3d ,,4 model with two non-commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non-commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjø rn and Catterall that stripes occur even in d = 2, although they imply the spontaneous breaking of the translation symmetry. [source] ## Towards effective Lagrangians for adelic strings FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-7 2009Article first published online: 20 MAR 200, B. DragovichAbstract p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these scalar field theories, obtained Lagrangians are also interesting in themselves. [source] ## Membranes, strings and integrability FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-7 2009C. KrishnanAbstract In the first half of this note, after briefly motivating and reviewing membrane field theories, we discuss their BPS funnel solutions. We discuss some aspects of embedding M-theory fuzzy funnels in these theories. In the second half, we focus on ABJM theory and discuss a test of AdS4/CFT3 based on integrability. We discuss a numerical mismatch at one loop in worldsheet perturbation theory and its possible resolutions. [source] ## Backreacting flavors in the Klebanov-Witten model via D7-branes FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2008Article first published online: 21 JUL 200, F. BeniniAbstract We discuss the addition of backreacting D7-branes to (fractional) D3-brane solutions in IIB supergravity which is dual to the addition of a large number of fields in the fundamental representation to known field theories in the Veneziano limit. We specialize to D7/D3-branes on the conifold (flavored Klebanov-Witten theory); we then generalize to massive flavors and to the case of fractional D3-branes and D7-branes with gauge flux (flavored Klebanov-Tseytlin theory). This talk is mainly based on [16, 18]. [source] ## Quantum field theories coupled to supergravity FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 3 2008J. GroßeAbstract This article is devoted to the investigation of the interplay of supersymmetric Yang,Mills theories (SYM) and supergravity (SUGRA). The topic is studied from two points of view: Firstly from the point of view of AdS/CFT correspondence, which realises the coupling of four dimensional superconformal ,, = 4 SYM theory and ten dimensional type IIB SUGRA in a holographic way. In order to arrive at theories that resemble quantum chromodynamics (QCD) more closely, fundamental fields are introduced using probe D7-branes and non-trivial background configuration are considered. In particular supergravity solutions that are only asymptotically anti-de Sitter and break supersymmetry are used. This allows the description of spontaneous chiral symmetry breaking. The meson spectrum is calculated and the existence of an associated Goldstone mode is demonstrated. Moreover it is shown that highly radially excited mesons are not degenerate. Additionally instanton configurations on the D7-branes are investigated, which lead to a holographic description of the dual field theory's Higgs branch. Finally a holographic description of heavy-light mesons is developed, which are mesons consisting of quarks with a large mass difference, such that a treatment of B mesons can be achieved The second approach is the technique of so-called space-time dependent couplings (also known as "local couplings"), where coupling constants are promoted to external sources. This allows to explore the conformal anomaly of quantum field theories coupled to a classical gravity background. The technique is extended to the superfield description of ,, = 1 supergravity, a complete basis for the anomaly is given and the consistency conditions that arise from a cohomological treatment are calculated. Possible implications for an extension of Zamolodchikov's c -theorem to four dimensional supersymmetric quantum field theories are discussed. [source] ## String theory: exact solutions, marginal deformations and hyperbolic spaces FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2 2007D. OrlandoAbstract This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces. [source] ## Heterotic strings on homogeneous spaces, FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 9 2005D. IsraëlAbstract We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS-NS 2-forms and gauge field fluxes. We give the general formalism and modular-invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S2 (already described in a previous paper) and the SU (3)/U(1)2 flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton. [source] ## Strings and D-branes in holographic backgrounds FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2005D. IsraëlAbstract We review recent progress in the study of non-rational (boundary) conformal field theories and their applications to describe exact holographic backgrounds in superstring theory. We focus mainly on the example of the supersymmetric coset SL(2, ,)/U(1), corresponding to the two-dimensional black hole, and its dual N = 2 Liouville. In particular we discuss the modular properties of their characters, their partition function as well as the exact boundary states for their various D-branes. Then these results are used to construct the corresponding quantities in the CFT of the NS5-brane background, with applications to Little String Theories. [source] ## Generalizations of the AdS/CFT correspondence, FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 8 2004I. KirschAbstract We consider generalizations of the AdS/CFT correspondence in which probe branes are embedded in gravity backgrounds dual to either conformal or confining gauge theories. These correspond to defect conformal field theories (dCFT) or QCD-like theories with fundamental matter, respectively. Moreover, starting from the dCFT we discuss the deconstruction of intersecting M5-branes and M-theory. We obtain the following results: i) Holography of defect conformal field theories. We consider holography for a general D3-Dp brane intersection in type IIB string theory (p , {3,5,7}). The corresponding near-horizon geometry is given by a probe AdS-brane in AdS5 × S5. The dual defect conformal field theory describes ,, = 4 super Yang-Mills degrees of freedom coupled to fundamental matter on a lower-dimensional space-time defect. We derive the spectrum of fluctuations about the brane embedding and determine the behaviour of correlation functions involving defect operators. We also study the dual conformal field theory in the case of intersecting D3-branes. To this end, we develop a convenient superspace approach in which both two- and four-dimensional fields are described in a two-dimensional (2,2) superspace. We show that quantum corrections vanish to all orders in perturbation theory, such that the theory remains a (defect) conformal field theory when quantized. ii) Flavour in generalized AdS/CFT dualities. We present a holographic non-perturbative description of QCD-like theories with a large number of colours by embedding D7-brane probes into two non-supersymmetric gravity backgrounds. Both backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the quark condensate and meson spectrum associated with these backgrounds. In the first background, we find some numerical evidence for a first order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the second, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson. iii) Deconstruction of extra dimensions. We apply the deconstruction method to the dCFT of intersecting D3-branes to obtain a field theory description for intersecting M5-branes. The resulting theory corresponds to two six-dimensional (2,0) superconformal field theories which we show to have tensionless strings on their four-dimensional intersection. Moreover, we argue that the SU(2)L R-symmetry of the dCFT matches the manifest SU(2) R-symmetry of the M5-M5 intersection. We finally explore the fascinating idea of deconstructing M-theory itself. We give arguments for an equivalence of M-theory on a certain background with the Higgs branch of a four-dimensional non-supersymmetric (quiver) gauge theory: in addition to a string theoretical motivation, we find wrapped M2-branes in the mass spectrum of the quiver theory at low energies. [source] ## Exact results in a non-supersymmetric gauge theory FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6-7 2004A. ArmoniWe consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to ,, = 1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1 / N). [source] ## Non-commutative field theories beyond perturbation theory FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003W. BietenholzWe investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm effect if we identify , = 1/B. Next we study the 3d , ,4 model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjø rn and Catterall that such stripes occur even in d = 2, although they imply the spontaneous breaking of translation symmetry. However, in d = 3 and d = 2 we observe only patterns of two stripes to be stable in the range of parameters investigated. [source] ## Boundaries, defects and Frobenius algebras FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003J. FuchsThe interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new computational tools. The construction of CFT correlators based on combining tools from topological field theory and non-commutative algebra in tensor categories, which we summarize in this contribution, allows e.g. to discuss, apart from boundary conditions, also defect lines and disorder fields. [source] ## Dynamical adjustment of propagators in Renormalization Group flows ANNALEN DER PHYSIK, Issue 3 2007M. SalmhoferAbstract A class of continuous renormalization group flows with a dynamical adjustment of the propagator is introduced and studied theoretically for fermionic and bosonic quantum field theories. The adjustment allows to include self,energy effects nontrivially in the denominator of the propagator and to adapt the scale decomposition to a moving singularity, and hence to define flows of Fermi surfaces in a natural way. These flows require no counterterms, but the counterterms used in earlier treatments can be constructed using them. The influence of propagator adjustment on the strong,coupling behaviour of flows is examined for a simple example, and some conclusions about the strong coupling behaviour of renormalization group flows are drawn. [source] ## Koopman-von Neumann formulation of classical Yang-Mills theories: I ANNALEN DER PHYSIK, Issue 3 2006P. CartaAbstract In this paper we present the Koopman-von Neumann (KvN) formulation of classical non-Abelian gauge field theories. In particular we shall explore the functional (or classical path integral) counterpart of the KvN method. In the quantum path integral quantization of Yang-Mills theories concepts like gauge-fixing and Faddeev-Popov determinant appear in a quite natural way. We will prove that these same objects are needed also in this classical path integral formulation for Yang-Mills theories. We shall also explore the classical path integral counterpart of the BFV formalism and build all the associated universal and gauge charges. These last are quite different from the analog quantum ones and we shall show the relation between the two. This paper lays the foundation of this formalism which, due to the many auxiliary fields present, is rather heavy. Applications to specific topics outlined in the paper will appear in later publications. [source] ## Comparisons and connections between mean field dynamo theory and accretion disc theory ASTRONOMISCHE NACHRICHTEN, Issue 1 2010E.G. BlackmanAbstract The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Generality with specificity: the dynamic field theory generalizes across tasks and time scales DEVELOPMENTAL SCIENCE, Issue 4 2008Vanessa R. SimmeringA central goal in cognitive and developmental science is to develop models of behavior that can generalize across both tasks and development while maintaining a commitment to detailed behavioral prediction. This paper presents tests of one such model, the Dynamic Field Theory (DFT). The DFT was originally proposed to capture delay-dependent biases in spatial recall and developmental changes in spatial recall performance. More recently, the theory was generalized to adults' performance in a second spatial working memory task, position discrimination. Here we use the theory to predict a specific, complex developmental pattern in position discrimination. Data with 3- to 6-year-old children and adults confirm these predictions, demonstrating that the DFT achieves generality across tasks and time scales, as well as the specificity necessary to generate novel, falsifiable predictions. [source] ## Beyond Dialogue: The Role of Science Within Theology DIALOG, Issue 3 2007Ernest L. SimmonsAbstract:, The purpose of this article is to provide background overview and contemporary context for the theme of this issue of Dialog, the role of science within theology. Over the last fifty years, this role has primarily involved dialogue and the drive to mutual understanding. That discussion has now reached a new stage seeking to move beyond dialogue toward what some are referring to as hypothetical consonance. One of the most serious constructive proposals moving beyond dialogue is Creative Mutual Interaction (CMI), proposed by Robert John Russell. The first five ways he discusses in CMI specifically address the role of science in theological reflection. It is argued that these five ways will assist the reader in contextualing the discussion found in the articles in this issue. Elaboration of each way is given, concluding with a constructive theological example of the heuristic use of scientific concepts found in quantum field theory. [source] ## Field theory for biogeography: a spatially explicit model for predicting patterns of biodiversity ECOLOGY LETTERS, Issue 1 2010James P. O'DwyerAbstract Predicting the variation of biodiversity across the surface of the Earth is a fundamental issue in ecology, and in this article we focus on one of the most widely studied spatial biodiversity patterns: the species,area relationship (SAR). The SAR is a central tool in conservation, being used to predict species loss following global climate change, and is striking in its universality throughout different geographical regions and across the tree of life. In this article we draw upon the methods of quantum field theory and the foundation of neutral community ecology to derive the first spatially explicit neutral prediction for the SAR. We find that the SAR has three phases, with a power law increase at intermediate scales, consistent with decades of documented empirical patterns. Our model also provides a building block for incorporating non-neutral biological variation, with the potential to bridge the gap between neutral and niche-based approaches to community assembly. Ecology Letters (2010) 13: 87,95 [source] ## Scattering of charged tensor bosons in gauge and superstring theories FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2010I. AntoniadisAbstract We calculate the leading-order scattering amplitude of one vector and two tensor gauge bosons in a recently proposed non-Abelian tensor gauge field theory and open superstring theory. The linear in momenta part of the superstring amplitude has identical Lorentz structure with the gauge theory, while its cubic in momenta part can be identified with an effective Lagrangian which is constructed using generalized non-Abelian field strength tensors. [source] ## Is N = 8 supergravity a finite field theory? FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-7 2009Article first published online: 21 APR 200, K.S. StelleAbstract Advances in calculational technique permit the study of ultraviolet structure in maximal super Yang-Mills and maximal supergravity theories at heretofore unattainable loop orders. Hints from string theory suggest that maximal supergravity might have a similar ultraviolet behavior in D = 4 spacetime dimensions as maximal super Yang-Mills theory and so be ultraviolet convergent. Yet what is known of field theoretic nonrenormalization theorems suggests only that -BPS counterterms are excluded. A key test of the relative finiteness properties of the two theories will be the ultraviolet divergences in D = 5 maximal supergravity at the four-loop level. [source] ## Towards effective Lagrangians for adelic strings FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-7 2009Article first published online: 20 MAR 200, B. DragovichAbstract p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these scalar field theories, obtained Lagrangians are also interesting in themselves. [source] ## The graviton propagator with a non-conserved external generating source FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 11-12 2007E.B. ManoukianAbstract A novel general expression is obtained for the graviton propagator from Lagrangian field theory by taking into account the necessary fact that in the functional differential approach of quantum field theory, in order to generate non-linearities in gravitation and interactions with matter, the external source T,,, coupled to the gravitational field, should a priori not be conserved ,,T,,, 0, so variations with respect to its ten components may be varied independently. The resulting propagator is the one which arises in the functional approach and does not coincide with the corresponding time-ordered product of two fields and it includes so-called Schwinger terms. The quantization is carried out in a gauge corresponding to physical states with two polarization states to ensure positivity in quantum applications. [source] ## Some aspects of c = -2 theory FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 11-12 2007M.A. RajabpourAbstract We investigate some aspects of the c = -2 logarithmic conformal field theory (LCFT). At first, we calculate some correlators of logarithmic conformal fields which have third order singular OPE with the energy-momentum tensor. Then, we argue about the fields in the c = -2 model which are associated with this kind of more general logarithmic primary fields. We go on to find fermionic representations for all the fields in the extended Kac table, in particular the untwisted sector. Moreover, we calculate the various OPEs of the fields, especially for the logarithmic energy-momentum tensor and by using these OPEs we find the exact finite transformation of this field. We briefly discuss about the important role of the zero modes in the c = -2 model. Finally we consider the perturbation of this theory and its relationship with integrable models, and generalization of Zamalodchikov's c-theorem. [source] |