Axial Vector Duality as a Gauge Symmetry and Topology Change in String Theory

TL;DR

The paper shows that axial–vector duality in abelian WZW cosets is an exact, residual gauge symmetry of string theory, and that marginal $J\\bar{J}$ deformations generate a continuous moduli line connecting backgrounds with different topology. By analyzing SU(2) and SL(2) WZW models (and generalizing to $G$), it demonstrates that the deformation line is governed by $O(2,2)$ rotations and that a discrete duality in $O(2,2,Z)$ implements $R\leftrightarrow 1/R$, mapping ends corresponding to vector and axial cosets. The torus partition function along the line remains invariant under duality, and the geometry along the line exhibits a smooth topology change (e.g., $S^3$ to $D_2\times S^1$), with endpoints equivalent under duality. The work further argues that such dualities are residual gauge symmetries in curved backgrounds and discusses extensions and open problems, including the full $O(d,d,Z)$ group and nonperturbative $\alpha'$ effects.

Abstract

Lines generated by marginal deformations of WZW models are considered. The Weyl symmetry at the WZW point implies the existence of a duality symmetry on such lines. The duality is interpreted as a broken gauge symmetry in string theory. It is shown that at the two end points the axial and vector cosets are obtained. This shows that the axial and vector cosets are equivalent CFTs both in the compact and the non-compact cases. Moreover, it is shown that there are $\s$-model deformations that interpolate smoothly between manifolds with different topologies.