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Article overview
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Free fermion resolution of supergroup WZNW models | Thomas Quella
; Volker Schomerus
; | Date: |
6 Jun 2007 | Abstract: | Extending our earlier work on PSL(2|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|N) along
with several close relatives such as PSL(N|N), certain Poincare supergroups and
the series OSP(2|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. | Source: | arXiv, arxiv.0706.0744 | Services: | Forum | Review | PDF | Favorites |
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