Symmetries of perturbed conformal field theories

TL;DR

This paper investigates how symmetries in conformal field theories are affected by perturbations, showing that D-branes preserve maximal possible symmetry during bulk deformations, with examples from WZW and Gepner models.

Contribution

It provides a detailed analysis of symmetry preservation in perturbed conformal field theories and examines the behavior of D-branes under such deformations.

Findings

Certain chiral algebra generators survive perturbations.

D-branes preserve maximal symmetry possible during bulk deformations.

Illustrated with examples from WZW and Gepner models.

Abstract

The symmetries of perturbed conformal field theories are analysed. We explain which generators of the chiral algebras of a bulk theory survive a perturbation by an exactly marginal bulk field. We also study the behaviour of D-branes under current-current bulk deformations. We find that the branes always continue to preserve as much symmetry as they possibly can, i.e. as much as is preserved in the bulk. We illustrate these findings with several examples, including permutation branes in WZW models and B-type D-branes in Gepner models.