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.

Towards a field theory of the plateau transitions in the integer quantum Hall effect

“…Recalling that the fermionic fields are 2×2 matrices, this leads to a level shift of 2 in the WZNW models defined over a and b. Such level shifts were also encountered in [34,40]. One obtains the following action for the PSL(2|2) WZNW model, in which the ellipsis indicates terms independent of a and b; these include the contributions of the bosonic fields α and β, the fermions λ ′′ and χ ′′ and ghosts.…”

“…The use of such decompositions is well established in the the free-field approach to WZNW models (see, for example [39] and references therein). In particular, such an approach has been followed in the study of the gl(n|n) current algebras and associated topological field theories [40]. We consider the gauged WZNW model 14 ,…”

gl(4|4) current superalgebra: Free field realization and screening currents

“…Note added: We became aware that free field realizations of sl(N|N) (or gl(N|N)) current algebra were investigated previously in [25,26]. There, the sl(N|N) k (or gl(N|N) k ) currents were expressed in terms of the sl(N) k−N and sl(N) −k−N currents and some b-c pairs.…”

Topological current algebras in two dimensions

“…The presence of dimension-three operators is an unavoidable consequence of having a non-abelian current algebra in our theory. We have found this type of topological symmetry in our study of the gl(N, N) affine Lie superalgebras [8]. Here we study this problem from a general point of view.…”