D-branes on a Deformation of SU(2)

TL;DR

This paper explores the behavior of D-branes in a family of conformal field theories connecting SU(2) WZW models and coset models, revealing symmetry breaking, flux quantization, and phase transitions.

Contribution

It provides a detailed analysis of D-branes' symmetry properties and phase transitions along a deformation line connecting different conformal field theories.

Findings

U(1) symmetry breaks to Z_k away from SU(2) point

Full U(1)×U(1) symmetry restored at SU(2) point

Indication of phase transitions for branes at angles

Abstract

We discuss D-branes on a line of conformal field theories connected by an exact marginal deformation. The line contains an SU(2) WZW model and two mutually T-dual SU(2)/U(1) cosets times a free boson. We find the D-branes preserving a U(1) isometry, an F-flux quantization condition and conformal invariance. Away from the SU(2) point a U(1) times U(1) symmetry is broken to U(1) times Z_k, i.e. continuous rotations of branes are accompanied by rotations along the branes. Requiring decoupling of the cosets from the free boson at the endpoints of the deformation breaks the continuous rotation of branes to Z_k. At the SU(2) point the full U(1) times U(1) symmetry is restored. This suggests the occurrence of phase transitions for branes at angles in the coset model, at a semiclassical level. We also discuss briefly the orientifold planes along the deformation line.