TT Deformations and Gravity

To understand the space of quantum field theories, we often begin with a tractable theory like a CFT and deform it by a local operator. When the operator is relevant, it generates an RG flow, which modifies the behavior of the theory in infrared. When the operator is exactly marginal, it parametrizes the moduli space of the CFT. However, the theory deformed by an irrelevant operator changes the UV behavior as well as the definition of the theory, so the resulting theory is usually difficult to understand. In this thesis, I study a very special example of an irrelevant deformation triggered by the TT operator in two dimensions and its relation to gravity, supersymmetry, and supergravity. I propose a manifestly supersymmetric version of the TT operator in superspace. In addition, I show that the deformed theory is classically equivalent to the undeformed theory coupled to two-dimensional gravity, which signals a deep connection to gravity. A closely related deformation appears in the holographic definition of supergravity solutions that interpolate between BTZ black holes and asymptotically linear dilaton backgrounds. This opens up the possibility of defining holography between non-AdS spacetimes and theories deformed by irrelevant deformations.