Marginal Deformations of WZNW and Coset Models from O(d,d) Transformation

TL;DR

This paper demonstrates how O(d,d) transformations induce marginal deformations in WZNW and coset models, linking algebraic transformations to specific current-current operators and extending the understanding of model deformations.

Contribution

It establishes a general connection between O(d,d) transformations and marginal deformations in WZNW models, including gauged versions, providing a unified framework for such deformations.

Findings

O(2,2) transformation yields marginal deformation via U(1) currents.

O(3,3) transformation relates to deformations of product models.

Proposes a general conjecture linking O(d,d) transformations to marginal deformations.

Abstract

We show that O(2,2) transformation of SU(2) WZNW model gives rise to marginal deformation of this model by the operator $\int d^2 z J(z)\bar J(\bar z)$ where $J$, $\bar J$ are U(1) currents in the Cartan subalgebra. Generalization of this result to other WZNW theories is discussed. We also consider O(3,3) transformation of the product of an SU(2) WZNW model and a gauged SU(2) WZNW model. The three parameter set of models obtained after the transformation is shown to be the result of first deforming the product of two SU(2) WZNW theories by marginal operators of the form $\sum_{i,j=1}^2 C_{ij} J_i \bar J_j$, and then gauging an appropriate U(1) subgroup of the theory. Our analysis leads to a general conjecture that O(d,d) transformation of any WZNW model corresponds to marginal deformation of the WZNW theory by combination of appropriate left and right moving currents belonging to the Cartan subalgebra; and O(d,d) transformation of a gauged WZNW model can be identified to the gauged version of such marginally deformed WZNW models.