Deformations, renormgroup, symmetries, AdS/CFT

Andrei Mikhailov

Published 2019-06-28Version 1

We consider the deformations of a supersymmetric quantum field theory by adding spacetime-dependent terms to the action. We propose to describe the renormgroup flow of such deformations as a solution of some Maurer-Cartan equation. In particular, we consider the strongly coupled limit of $N=4$ supersymmetric Yang-Mills theory. The AdS/CFT correspondence relates the computation of the renormgroup flow to a computation in the classical supergravity, which we describe. There is a leg amputation procedure, which constructs a solution of the Maurer-Cartan equation from tree diagramms of SUGRA. We consider a particular example of the beta-deformation. It is known that the leading term of the beta-function is cubic in the parameter of the beta-deformation. We give a cohomological interpretation of this leading term. We conjecture that it is actually encoded in some simpler cohomology class, which is quadratic in the parameter of the beta-deformation.