SEZIONE DI FIRENZE
Seminario di Matteo Bertolini (SISSA)
Conformal manifolds are families of conformal field Theories connected by exactly marginal deformations. They are ubiquitous in theories with supersymmetry,while there are no examples, at least in d>2, in non-supersymmetric setups. One can question whether they can ever exists. In this talk I address these issues by looking at the constraints that a conformal field theory should enjoy to admit exactly marginal deformations. In particular, using tools from conformal perturbation theory, I derive a sum rule the CFT should satisfy, and discuss some of the implications that this has on the CFT spectrum and OPE coefficients.
Then, I will focus on conformal field theories admitting a gravity dual description, and as such a large-N expansion. I will discuss the relation between conformal perturbation theory and loop expansion in the bulk, and show how such connection could help in the search for non-supersymmetric) conformal manifolds beyond the planar limit. Using a toy-example I will show that this is not an empty set.