Boundary conditions for SU(2) Yang-Mills on AdS(4)

Abstract

We consider SU(2) Yang-Mills theory on AdS(4) by imposing various boundary conditions, which correspond to non-trivial deformations of its boundary CFT. We obtain classical solutions of Yang-Mills fields up to the first subleading order correction by using small amplitude expansion of the gauge field without considering gravitational back reaction. We also consider SU(2) Yang-Mills instanton solution in AdS(4) bulk, and propose a boundary action. It turns out that the boundary theory is the Chern Simons theory with a non-local deformation which has the form similar to the Wilson line. In the limit of the deformation parameter rho -˃ infinity, this non-local deformation is suppressed and the boundary theory becomes pure Chern Simons. For large but finite values of rho, tins non-local deformation can be treated perturbatively within the Chern-Simon theory.