A Field Theory of Currents

Sugawara, Hirotaka

doi:10.1103/physrev.170.1659

Cited by 453 publications

(225 citation statements)

References 8 publications

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“…The central extension is determined by the invariant metric (2.3). The current superalgebra above defines a chiral vertex algebra via the Sugawara construction [57]. As usual, the corresponding energy momentum tensor is obtained by contracting the currents with the inverse of a distinguished invariant and non-degenerate metric.…”

Section: Covariant Formulation Of the Symmetrymentioning

confidence: 99%

Free fermion resolution of supergroup WZNW models

Quella

Schomerus²

2007

J. High Energy Phys.

132

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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 Poincaré supergroups and the series OSP (2|2N ). The technical foundation for this remarkable progress is a special Feigin-Fuchs type representation which allows to keep the bosonic symmetry manifest instead of reducing it to free fields. In preparation for the field theory analysis, we shall exploit a minisuperspace analogue of the resulting 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.

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Section: Covariant Formulation Of the Symmetrymentioning

confidence: 99%

Free fermion resolution of supergroup WZNW models

Quella

Schomerus²

2007

J. High Energy Phys.

132

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“…It is to be hoped then that the techniques of nonrelativistic current algebra can be carried over and incorporated into the study of relativistic models (1,(7)(8)(9)(10) ..…”

mentioning

confidence: 99%

Non-relativistic current algebra in the N/V limit

Goldin¹,

Grodnik²,

Powers³

et al. 1973

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“…The operators are not built from an enveloping algebra as in the Sugawara constructions [30] but instead exists in their own right. For example in the section 4.1 the operators, D(x), satisfy the same operator product expansions as one has in Virasoro theories [12] which is built from a lattice.…”

Section: Discussionmentioning

confidence: 99%