gl(N,N) Current Algebras and Topological Field Theories

Abstract

The conformal field theory for the $gl(N,N)$ affine Lie superalgebra in two space-time dimensions is studied. The energy-momentum tensor of the model, with vanishing Virasoro anomaly, is constructed. This theory has a topological symmetry generated by operators of dimensions 1, 2 and 3, which are represented as normal-ordered products of $gl(N,N)$ currents. The topological algebra they satisfy is linear and differs from the one obtained by twisting the $N=2$ superconformal models. It closes with a set of $gl(N)$ bosonic and fermionic currents. The Wess-Zumino-Witten model for the supergroup $GL(N,N)$ provides an explicit realization of this symmetry and can be used to obtain a free-field representation of the different generators. In this free-field representation, the theory decomposes into two uncoupled components with $sl(N)$ and $U(1)$ symmetries. The non-abelian component is responsible for the extended character of the topological algebra, and it is shown to be equivalent to an $SL(N)/SL(N)$ coset model. In the light of these results, the $G/G$ coset models are interpreted as topological sigma models for the group manifold of $G$

53 pages

References in corpus (6)

• Topological Matter in Two Dimensions
• $G/G$--Topological Field Theories by Cosetting $G_k$
• G/G Models and W_N strings
• c=1 String Theory as a Topological G/G Model
• Topological current algebras in two dimensions
• On Moduli Space of C=0 Topological Conformal Field Theories

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• Wess-Zumino-Novikov-Witten Models Based on Lie Superalgebras
• Primary fields and screening currents of gl(2|2) non-unitary conformal field theory
• Coherent State Construction of Representations of osp(2|2) and Primary Fields of osp(2|2) Conformal Field Theory
• A Bosonization of $U_q(\widehat{sl}(M|N))$
• Superconformal current algebras and topological field theories
• Knots in $SU\left(M|N\right)$ Chern-Simons Field Theory