Abstract
Extending our earlier work on PSL(2 vertical stroke 2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M vertical stroke N) along with several close relatives such as PSL(N vertical stroke N), certain Poincar'e supergroups and the series OSP(2 vertical stroke 2N). This remarkable progress relies on the use of a special Feigin-Fuchs type representation. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of a free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.
Citation Formats
Quella, T, and Schomerus, V.
Free fermion resolution of supergroup WZNW models.
Germany: N. p.,
2007.
Web.
Quella, T, & Schomerus, V.
Free fermion resolution of supergroup WZNW models.
Germany.
Quella, T, and Schomerus, V.
2007.
"Free fermion resolution of supergroup WZNW models."
Germany.
@misc{etde_20902982,
title = {Free fermion resolution of supergroup WZNW models}
author = {Quella, T, and Schomerus, V}
abstractNote = {Extending our earlier work on PSL(2 vertical stroke 2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M vertical stroke N) along with several close relatives such as PSL(N vertical stroke N), certain Poincar'e supergroups and the series OSP(2 vertical stroke 2N). This remarkable progress relies on the use of a special Feigin-Fuchs type representation. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of a free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.}
place = {Germany}
year = {2007}
month = {Jun}
}
title = {Free fermion resolution of supergroup WZNW models}
author = {Quella, T, and Schomerus, V}
abstractNote = {Extending our earlier work on PSL(2 vertical stroke 2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M vertical stroke N) along with several close relatives such as PSL(N vertical stroke N), certain Poincar'e supergroups and the series OSP(2 vertical stroke 2N). This remarkable progress relies on the use of a special Feigin-Fuchs type representation. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of a free fermion construction to deduce the spectrum of the Laplacian on type I supergroups. The latter is shown to be non-diagonalizable. After lifting these results to the full WZNW model, we address various issues of the field theory, including its modular invariance and the computation of correlation functions. In agreement with previous findings, supergroup WZNW models allow to study chiral and non-chiral aspects of logarithmic conformal field theory within a geometric framework. We shall briefly indicate how insights from WZNW models carry over to non-geometric examples, such as e.g. the W(p) triplet models.}
place = {Germany}
year = {2007}
month = {Jun}
}