Current-Current Deformations of Conformal Field Theories, and WZW Models

TL;DR

The paper analyzes moduli spaces of conformal field theories generated by current-current perturbations, establishing that exact deformations correspond to pseudo-orthogonal transformations of charge lattices and can be described by ${\rm O}(d,\bar{d})/{\rm O}(d)\times{\rm O}(ar{d})$ actions. It then specializes to WZW models, elucidating a finite duality group structure and an orbifold/coset representation that connects current-current deformations to toroidal data. A sigma-model construction via asymmetric gauging and axial-vector duality yields explicit WZW-like actions with deformed metrics, $B$-fields, and a nontrivial dilaton, and the Hamiltonian analysis confirms a dip in the generalized Laplacian $\Delta^{\Phi}$ consistent with conformal invariance. The ${\rm SU}(2)$ example provides a concrete realization of the deformation procedure and spectrum matching. Together, the results give a concrete bridge between CFT deformation theory and sigma-model realizations for current-current deformations of WZW models, with implications for D-branes and broader moduli-space geometry.

Abstract

Moduli spaces of conformal field theories corresponding to current-current deformations are discussed. For WZW models, CFT and sigma model considerations are compared. It is shown that current-current deformed WZW models have WZW-like sigma model descriptions with non-bi-invariant metrics, additional B-fields and a non-trivial dilaton.