Perturbative deformations of conformal field theories revisited

TL;DR

This paper explores how to systematically exponentiate perturbations in conformal field theories, revealing algebraic obstructions in some models and explaining these phenomena through renormalization analysis.

Contribution

It develops a canonical mathematical framework for exponentiating perturbations in conformal field theories and applies it to specific models, uncovering algebraic obstructions.

Findings

Obstructions to exponentiating perturbations in the quintic model

No obstructions in the quartic model

Renormalization analysis explains the observed obstructions

Abstract

We investigate the moduli space of conformal field theories by setting up a canonical mathematical process for exponentiating perturbations corresponding to critical fields. We apply this process to the free field theory and the Gepner models of the Fermat quintic and quartic. We find algebraic obstructions to exponentiating purely perturbative deformations in the case of the quintic, while in the case of the quartic the obstructions vanish. While this result may seem surprising at first, we find an explanation of these effects via the renormalization analysis of Nemeschansky-Sen.