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

Dileep P. Jatkar; Jae-Hyuk Oh

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

Dileep P. Jatkar, Jae-Hyuk Oh

High Energy Physics - Theory · Submitted 9 Mar 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.91 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.13 · mentions code or data availability 0.01.

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider SU(2) Yang-Mills theory on $AdS_4$ by imposing various boundary conditions, which correspond to non-trivial deformations of its boundary $CFT$.	contribution 0.91	0.89	0.08	asserted 1.00
s1	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.	method 0.84	0.95	0.06	asserted 1.00
s2	We also consider SU(2) Yang-Mills instanton solution in $AdS_4$ bulk, and propose a boundary action.	contribution 1.00	0.91	0.07	asserted 0.91
s3	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.	result 0.95	0.88	0.52	asserted 1.00
s4	In the limit of the deformation parameter $\rho \rightarrow \infty$, this non-local deformation is suppressed and the boundary theory becomes pure Chern Simons.	result 0.86	0.82	0.19	asserted 1.00
s5	For large but finite values of $\rho$, this non-local deformation can be treated perturbatively within the Chern-Simon theory.	result 0.49	0.73	0.11	hedged possibility 0.54

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Original 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.

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8 arXiv papers cite this in 9 sentences

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Papers citing it · 3 sentences without a confident label

Cites it as background 6 papers

Studies on such theories are given in [ref] ] , $ℝ^d ×[0,∞)$.

Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS$_{4}$ · A short introduction to conformally coupled scalar theory in AdS space · 0.96
Since the unitarity bound of the scalar operators in CFT is $Δ≥d/2-1$, two point correlation functions in both CFTs are positive definite [There are many discussions about alternative quantization schemes in Dirac field [ref] , Rarita-Schwinger field [ref] , $U(1)$ gauge field [ref] and $SU(2)$ Yang-Mills field [ref] .].

Boundary conditions for conformally coupled scalar in AdS$_4$ · Introduction · 0.85
Especially, studies on holographic renormalization of marginal operators [ref] and holographic renormalization in asymptotically Lifshitz spacetime [ref] are interesting.

Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation · Introduction · 0.99

What it cites · 25 sentences without a confident label

Builds on 1 paper

We will discuss generalizations of other deformations which in the abelian context were considered in [ref] .

Electric-magnetic Duality and Deformations of Three-Dimensional CFT's · Introduction · 0.94

Cites as background 5 papers

Klebanov and Witten [ref] first discussed it in AdS/CFT, providing interesting boundary conformal field theories generated by the alternate scheme [ref] .

Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence · Introduction · 0.95
Klebanov and Witten [ref] first discussed it in AdS/CFT, providing interesting boundary conformal field theories generated by the alternate scheme [ref] .

A Note on Multi-trace Deformations and AdS/CFT · Introduction · 0.95
Klebanov and Witten [ref] first discussed it in AdS/CFT, providing interesting boundary conformal field theories generated by the alternate scheme [ref] .

AdS/CFT Correspondence and Symmetry Breaking · Introduction · 0.95

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