Topological current algebras in two dimensions

Isidro, J. M.; Ramallo, Alfonso V.

doi:10.1016/0370-2693(93)91033-j

Cited by 10 publications

(31 citation statements)

References 23 publications

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“…Indeed, if α a are c-number constants, one can redefine T , G and R as follows: (W, V ) is realised. A similar conclusion has also been reported in [4] for the bosonic case (i.e., when d F = 0), but our presentation here is totally general. An earlier reference on gauged WZW models is [31].…”

Section: )supporting

confidence: 91%

The BRST Symmetry of Affine Lie Superalgebras and Noncritical Strings

Ennes

Ramallo

Isidro

1996

Int. J. Mod. Phys. A

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Section: )supporting

confidence: 91%

The BRST Symmetry of Affine Lie Superalgebras and Noncritical Strings

Ennes

Ramallo

Isidro

1996

Int. J. Mod. Phys. A

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“…This means that our extended topological algebra is realized in this type of topological theories which, from our point of view, are regarded as topological sigma models for group manifolds, i.e., as the topological analogue of the Wess-Zumino-Witten theories. These aspects of our construction will be discussed elsewhere [26]. This paper is organized as follows.…”

Section: Introduction and Summary Of Main Resultsmentioning

confidence: 99%

gl(N, N) current algebras and topological field theories

Isidro

Ramallo

1994

Nuclear Physics B

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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.

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“…However, at level k = −2N (or more generally −2g ∨ ) this operator commutes with all the Kač-Moody currents and therefore does not affect the correlation functions -see Appendix 6 of reference [12] and note the different sign conventions for the level k. In a more general framework, the WZNW models at level k = −2g ∨ arise quite naturally in both two-dimensional (c = 0) topological field theories possessing a non-Abelian current algebra [79], and in the strong disorder treatment of arbitrary WZNW models coupled to random vector potentials [39]. The critical level arises from a BRST (Becchi-Rouet-Stora-Tyutin) [80,81] symmetry nilpotency condition and is required for the coexistence of a Kač-Moody algebra symmetry and a topological algebra symmetry [79]. We emphasize that the level of the underlying Kač-Moody algebra, the existence of a topological algebra and the stability of our strongly disordered theory are therefore intimately related.…”

Section: Approach Fermions Bosonsmentioning

confidence: 99%

Disordered Dirac fermions: the marriage of three different approaches

Bhaseen¹,

Caux²,

Kogan³

et al. 2001

Nuclear Physics B

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We compare the critical multipoint correlation functions for twodimensional (massless) Dirac fermions in the presence of a random su(N ) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous results obtained using the replica approach and in the limit of infinite disorder strength and compare them to new results (presented here) obtained using the supersymmetric approach to the N = 2 case. We demonstrate that this ménageà trois of different approaches leads to identical results. Remarkable relations between apparently different conformal field theories (CFTs) are thereby obtained. We further establish a connection between the random Dirac fermion problem and the c = −2 theory of dense polymers. The presence of the c = −2 theory may be seen in all three different treatments of the disorder. PACS: 72.15.Rh, 71.30.+h

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Topological current algebras in two dimensions

Cited by 10 publications

References 23 publications

The BRST Symmetry of Affine Lie Superalgebras and Noncritical Strings

The BRST Symmetry of Affine Lie Superalgebras and Noncritical Strings

gl(N, N) current algebras and topological field theories

Disordered Dirac fermions: the marriage of three different approaches

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