Conformal current algebra in two dimensions

Abstract

To cite this article: Sujay K. Ashok et al JHEP06(2009) Abstract: We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing Killing form, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two-and threepoint functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of P SU (n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.

The Hirota equation for string theory in AdS5 × S5 from the fusion of line operators

“…There is at least one family of models where this is the case: the non-linear sigma-models on the supergroup P Sl(n|n). This was shown in [32], building up on earlier studies of these models [33] [34]. This result is relevant for string theory in AdS 3 × S 3 , supported by RR and/or NS fluxes.…”

Fermionic coset, critical level $ \mathcal{W}_4^{{(2)}} $ -algebra and higher spins

“…Also perturbations of current-current type are explored. It is possible to compute the spectra of perturbed theories [49][50][51], to compute some correlation functions [52,55,56] and to establish Yangian symmetry [53].…”

“…If the Killing form of the underlying Lie super algebra vanishes, then current-current perturbations are truly marginal. Further they are under good control and physical quantities can be computed [49][50][51][52][53][54][55][56]. So in principle one can apply the results of these works to the nonlinear A-model.…”

Asymptotic symmetries of string theory onAdS3×S3with Ramond-Ramond fluxes

“…In that formalism the central part of the worldsheet model is the sigma-model on the P SU (1, 1|2) supergroup (or rather, its universal cover), which contains a bosonic AdS 3 ×S 3 subspace. The main building block in constructing the vertex operators of the spacetime symmetry generators are the curents of the P SU (1, 1|2) supergroup model which satisfy a conformal current algebra found in [12]. Technically, our analysis is a non-chiral version of the construction of the super Virasoro algebra in [9,10,13] for the case of F1-NS5 backgrounds.…”