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 (19)

• A Stress Tensor for Anti-de Sitter Gravity
• AdS/CFT Correspondence and Symmetry Breaking
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• SL(2,Z) Action on Three-Dimensional CFTs and Holography
• A Note on Multi-trace Deformations and AdS/CFT
• States and Boundary Terms: Subtleties of Lorentzian AdS/CFT
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4
• Boundary terms in the AdS/CFT correspondence for spinor fields
• Lectures on instantons
• New Massive Gravity and AdS_4 counterterms
• Free Spin 2 Duality Invariance Cannot be Extended to GR
• A Note on AdS/CFT Dual of SL(2,Z) Action on 3D Conformal Field Theories with U(1) Symmetry
• Regular and Irregular Boundary Conditions in the AdS/CFT Correspondence
• Note on the boundary terms in AdS/CFT correspondence for Rarita-Schwinger field
• Electric-magnetic Duality and Deformations of Three-Dimensional CFT's

Cited by in corpus (8)

• Stochastic quantization and holographic Wilsonian renormalization group
• Stochastic quantization of conformally coupled scalar in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of massless fermions in AdS
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass
• Electric-magnetic duality implies (global) conformal invariance
• Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation
• Electric-magnetic duality as a quantum operator and more symmetries of $U(1)$ gauge theory
• Boundary conditions for conformally coupled scalar in AdS${}_4$