Continuous Family of Conformal Field Theories and Exactly Marginal Operators

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.