Conformal Field Theories: From Old to New

TL;DR

This paper reviews recent methods for constructing new conformal field theories from existing ones by introducing new stress tensors, resulting in novel spin-two gauge theories, exemplified by gauged sigma models.

Contribution

It introduces a general approach to generate new conformal field theories via modifications in the chiral algebra, particularly through new stress tensors, expanding the landscape of conformal models.

Findings

New conformal theories can be constructed from old ones using additional stress tensors.

The resulting theories are often new spin-two gauge theories.

Explicit example: gauged sigma models derived from conformal non-linear sigma models.

Abstract

In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new conformal stress tensors in its chiral algebra, and it turns out that the new conformal field theory is generically a new spin-two gauge theory. As an example we discuss the new spin-two gauged sigma models which arise in this fashion from the general conformal non-linear sigma model.