| Abstract: Many supersymmetric CFTs possess a continuous space of vacua, known as a moduli space. A long-standing open problem is to determine whether a CFT has a moduli space using only its CFT data, without using a Lagrangian description. In this talk, we make progress towards resolving this question. First, assuming a continuous global symmetry is spontaneously broken on the moduli space, we identify a universal necessary condition on the CFT data for it to have a moduli space. Then, in the generic case, we employ an analytic bootstrap equation to derive perturbative sum rules that constrain the data of any CFT with a moduli space. This talk is based on joint work with G. Cuomo and L. Rastelli. |