Super Yang-Mills theories with inhomogeneous mass deformations

Yoonbai Kim (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 16419, South Korea) ; O-Kab Kwon (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 16419, South Korea) ; D. Tolla (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 16419, South Korea; University College, Sungkyunkwan University, Suwon, 16419, South Korea)

We construct the 4-dimensional N = 1 2 $$ \mathcal{N}=\frac{1}{2} $$ and N $$ \mathcal{N} $$ = 1 inhomogeneously mass-deformed super Yang-Mills theories from the N $$ \mathcal{N} $$ = 1* and N $$ \mathcal{N} $$ = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the N $$ \mathcal{N} $$ = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the N = 1 2 $$ \mathcal{N}=\frac{1}{2} $$ theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

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      "surname": "Kwon", 
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      "value": "We construct the 4-dimensional   <math> <mi>N</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \\mathcal{N}=\\frac{1}{2} $$  and   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 1 inhomogeneously mass-deformed super Yang-Mills theories from the   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 1* and   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the   <math> <mi>N</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \\mathcal{N}=\\frac{1}{2} $$  theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions."
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Published on:
09 December 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 12
Pages 1-21
DOI:
https://doi.org/10.1007/JHEP12(2020)060
arXiv:
2008.00868
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: