Continuous Family of Conformal Field Theories and Exactly Marginal Operators

TL;DR

This paper demonstrates that the existence of a conformal manifold implies the presence of exactly marginal operators, which can be derived from conformal interfaces, using a model-independent approach grounded in conformal symmetry.

Contribution

It establishes a general, model-independent method to reconstruct exactly marginal operators from conformal interfaces connecting nearby CFTs.

Findings

Exactly marginal operators can be reconstructed from conformal interfaces.

The existence of a conformal manifold implies the presence of exactly marginal operators.

The construction is based on conformal symmetry principles and is model-independent.

Abstract

Does a conformal manifold imply the existence of exactly marginal operators? We answer this question affirmatively under the assumption that there exists a conformal interface with certain properties connecting nearby CFTs. We show that the exactly marginal operator that connects the CFTs can be reconstructed from the interface displacement operator. Our construction is model-independent and based on the general principles of conformal symmetry.