Boundary conditions for SU(2) Yang-Mills on $Ad{S}_4$

Abstract

We consider SU(2) Yang-Mills theory on $Ad{S}_4$ 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 $Ad{S}_4$ 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 $\rho \to \infty$, 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.

1+30 pages, a new section about SU(2) Yang-Mills version of electric-magnetic duality and the related references are added; Journal of High Energy Physics, Volume 2012, Issue 8

References in corpus (6)

• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Lectures on instantons
• New Massive Gravity and AdS_4 counterterms
• Electric-magnetic Duality and Deformations of Three-Dimensional CFT's

Cited by in corpus (1)

• Stochastic quantization and holographic Wilsonian renormalization group