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arXiv · 1203.2106

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

Dileep P. Jatkar·Jae-Hyuk Oh
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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 $ρ\rightarrow \infty$, this non-local deformation is suppressed and the boundary theory becomes pure Chern Simons. For large but finite values of $ρ$, this non-local deformation can be treated perturbatively within the Chern-Simon theory.

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Dileep P. Jatkar, Jae-Hyuk Oh. 2012-10-05. Boundary conditions for SU(2) Yang-Mills on $AdS_4$. https://doi.org/10.1007/jhep08(2012)077

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