Boundary conditions for SU(2) Yang-Mills on $AdS_4$

TL;DR

This paper explores boundary conditions for SU(2) Yang-Mills theory on AdS4, deriving classical solutions, analyzing instantons, and proposing a boundary action that links to a deformed Chern-Simons theory.

Contribution

It introduces a novel boundary action for SU(2) Yang-Mills on AdS4 and connects boundary deformations to a non-local Chern-Simons theory with a Wilson line-like term.

Findings

Classical solutions obtained up to first subleading order.

Boundary theory is a non-local deformation of Chern-Simons.

Deformation suppressed as parameter $ ho ightarrow ext{infinity}$.

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 $\rho \rightarrow \infty$, this non-local deformation is suppressed and the boundary theory becomes pure Chern Simons. For large but finite values of $\rho$, this non-local deformation can be treated perturbatively within the Chern-Simon theory.