The Tilting Space of Boundary Conformal Field Theories

TL;DR

This paper explores the geometric structure of boundary conformal field theories, revealing they form coset spaces and providing explicit examples with free fields, thus enhancing understanding of conformal manifolds.

Contribution

It demonstrates that boundary conformal field theories' conformal manifolds have a coset structure and provides detailed examples with free fields, extending to more complex theories.

Findings

Conformal manifolds in boundary CFTs have a coset structure.

Explicit examples with free scalar and spinor fields are worked out.

The results generalize to interacting and more complex theories.

Abstract

In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out examples in the case of free fields of spin zero and one-half. These results give a simple illustration of the salient features of conformal manifolds while generalising to interacting and more intricate setups. Our work was inspired by [2203.17157]