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## Gauge Group (gauge + group)
## Selected Abstracts## Compactifications of the heterotic string with unitary bundles FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 11 2006T. WeigandAbstract We describe a large new class of four-dimensional supersymmetric string vacua defined as compactifications of the E8 × E8 and the SO(32) heterotic string on smooth Calabi-Yau threefolds with unitary gauge bundles and heterotic five-branes. The conventional gauge symmetry breaking via Wilson lines is replaced by the embedding of non-flat line bundles into the ten-dimensional gauge group, thus opening up the way for phenomenologically interesting string compactifications on simply connected manifolds. After a detailed analysis of the four-dimensional effective theory we exemplify the general framework by means of a couple of explicit examples involving the spectral cover construction of stable holomorphic bundles. As for the SO(32) heterotic string, the resulting vacua can be viewed, in the S-dual Type I picture, as a generalisation of magnetized D9/D5-brane models. In the case of the E8 × E8 string, we find a natural way to construct realistic MSSM-like models, either directly or via a flipped SU(5) GUT scenario. [source] ## Compactifications on half-flat manifolds, FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 3 2005S. GurrieriAbstract We review various aspects of compactifications of heterotic and type II supergravities on six dimensional manifolds. In the general framework of non-Kähler compactifications, emphasis is made on a particular class of manifolds with SU(3)-structure named half-flat. We recall how these manifolds appeared in the context of mirror symmetry of type II theories, providing mirror configurations to Calabi-Yau compactifications with NS-NS electric fluxes. In the heterotic sector, they generate a potential for all moduli, and are expected to break the E8 × E8 gauge group down to SO(10) × E8 in 4 dimensions. [source] ## On the absence of large-order divergences in superstring theory FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 1 2003S. DavisThe genus-dependence of multi-loop superstring amplitudes is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string perturbation theory, a result which is based only on the supersymmetric generalization of the Polyakov measure and not the gauge group of the string model. [source] ## (0,2) Gauged linear sigma model on supermanifold ANNALEN DER PHYSIK, Issue 7-8 2009Y. OkameAbstract We construct (0,2), D = 2 gauged linear sigma model on supermanifold with both an Abelian and non-Abelian gauge symmetry. For the purpose of checking the exact supersymmetric (SUSY) invariance of the Lagrangian density, it is convenient to introduce a new operator for the Abelian gauge group. The operator provides consistency conditions for satisfying the SUSY invariance. On the other hand, it is not essential to introduce a similar operator in order to check the exact SUSY invariance of the Lagrangian density of non-Abelian model, contrary to the Abelian one. However, we still need a new operator in order to define the (0,2) chirality conditions for the (0,2) chiral superfields. The operator can be defined from the conditions assuring the (0,2) supersymmetric invariance of the Lagrangian density in superfield formalism for the (0,2) U(N) gauged linear sigma model. We found consistency conditions for the Abelian gauge group which assure (0,2) supersymmetric invariance of Lagrangian density and agree with (0,2) chirality conditions for the superpotential. The supermanifold ,m|n becomes the super weighted complex projective space WCPm-1|n in the U(1) case, which is considered as an example of a Calabi-Yau supermanifold. The superpotential W(,,,) for the non-Abelian gauge group satisfies more complex condition for the SU(N) part, except the U(1) part of U(N), but does not satisfy a quasi-homogeneous condition. This fact implies the need for taking care of constructing the Calabi-Yau supermanifold in the SU(N) part. Because more stringent restrictions are imposed on the form of the superpotential than in the U(1) case, the superpotential seems to define a certain kind of new supermanifolds which we cannot identify exactly with one of the mathematically well defined objects. [source] ## (0,2) Gauged linear sigma model on supermanifold ANNALEN DER PHYSIK, Issue 7-8 2009Y. OkameAbstract We construct (0,2), D = 2 gauged linear sigma model on supermanifold with both an Abelian and non-Abelian gauge symmetry. For the purpose of checking the exact supersymmetric (SUSY) invariance of the Lagrangian density, it is convenient to introduce a new operator for the Abelian gauge group. The operator provides consistency conditions for satisfying the SUSY invariance. On the other hand, it is not essential to introduce a similar operator in order to check the exact SUSY invariance of the Lagrangian density of non-Abelian model, contrary to the Abelian one. However, we still need a new operator in order to define the (0,2) chirality conditions for the (0,2) chiral superfields. The operator can be defined from the conditions assuring the (0,2) supersymmetric invariance of the Lagrangian density in superfield formalism for the (0,2) U(N) gauged linear sigma model. We found consistency conditions for the Abelian gauge group which assure (0,2) supersymmetric invariance of Lagrangian density and agree with (0,2) chirality conditions for the superpotential. The supermanifold ,m|n becomes the super weighted complex projective space WCPm-1|n in the U(1) case, which is considered as an example of a Calabi-Yau supermanifold. The superpotential W(,,,) for the non-Abelian gauge group satisfies more complex condition for the SU(N) part, except the U(1) part of U(N), but does not satisfy a quasi-homogeneous condition. This fact implies the need for taking care of constructing the Calabi-Yau supermanifold in the SU(N) part. Because more stringent restrictions are imposed on the form of the superpotential than in the U(1) case, the superpotential seems to define a certain kind of new supermanifolds which we cannot identify exactly with one of the mathematically well defined objects. [source] |