On deformations of 2d SCFTs

TL;DR

This paper explores continuous deformations of 2D superconformal field theories that preserve algebraic structures, revealing connections to string backgrounds, vertex operators, and dualities.

Contribution

It introduces a general framework for deformations of super Virasoro constraints, linking them to string backgrounds and symmetries.

Findings

Deformations preserving superconformal algebra are characterized.

Massless NS and NS-NS backgrounds are realized through specific deformations.

Hints at a realization of S-duality via algebra isomorphisms.

Abstract

Motivated by the representation of the super Virasoro constraints as generalized Dirac-K{\"a}hler constraints $(d \pm d^\dagger)|\psi> = 0$ on loop space, examples of the most general continuous deformations $d \to e^{-W} d e^W$ are considered which preserve the superconformal algebra at the level of Poisson brackets. The deformations which induce the massless NS and NS-NS backgrounds are exhibited. Hints for a manifest realization of S-duality in terms of an algebra isomorphism are discussed. It is shown how the first order theory of 'canonical deformations' is reproduced and how the deformation operator $W$ encodes vertex operators and gauge transformations.