Operator Deformations and T-duality via Parallel Transport

TL;DR

This paper introduces a novel approach to understanding operator deformations and T-duality in quantum field theories through the concept of parallel transport in moduli space, extending beyond conformal theories.

Contribution

It develops a framework for computing operator deformations via parallel transport and applies it to realize T-duality differently from traditional methods.

Findings

Operator deformations can be systematically computed using parallel transport.

T-duality can be understood through this new geometric perspective.

The approach extends to non-conformal quantum field theories.

Abstract

We consider deformations of CFTs from the perspective of parallel transport in moduli space. In particular, we show how the deformations of individual operators can be computed and we also explore how these ideas can be extended to more general QFTs lacking conformal symmetry. We explore how to write one theory in terms of operators defined in a nearby theory, related to the first by a parallel transport in theory space. Using this construction, we describe how T-duality can be realised and how this provides a different perspective from the usual Buscher construction.