Twisted circle compactification of $\mathcal{N}=4$ SYM and its Holographic Dual
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| Format: | Preprint |
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2024
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| author | Kumar, S. Prem Stuardo, Ricardo |
| author_facet | Kumar, S. Prem Stuardo, Ricardo |
| contents | We consider a compactification of 4D $\mathcal{N}=4$ SYM, with $SU(N)$ gauge group, on a circle with anti-periodic boundary conditions for the fermions. We couple the theory to a constant background gauge field along the circle for an abelian subgroup of the $R$-symmetry which allows to preserve four supersymmetries. The 3D effective theory exhibits gapped and ungapped phases, which we argue are holographically dual, respectively, to a supersymmetric soliton in AdS$_{5}\times S^{5}$, and a particular quotient of AdS$_5\times S^5$. The gapped phase corresponds to an IR 3D $\mathcal{N}=2$ supersymmetric Yang-Mills-Chern-Simons theory at level $N$, while the ungapped phase is naturally identified with the root of a Higgs branch in the 3D theory. We discuss the extension of the twisting procedure to maximally SUSY Yang-Mills theories in different dimensions, obtaining the relevant duals for 2D and 6D, and comment on the odd dimensional cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03739 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted circle compactification of $\mathcal{N}=4$ SYM and its Holographic Dual Kumar, S. Prem Stuardo, Ricardo High Energy Physics - Theory We consider a compactification of 4D $\mathcal{N}=4$ SYM, with $SU(N)$ gauge group, on a circle with anti-periodic boundary conditions for the fermions. We couple the theory to a constant background gauge field along the circle for an abelian subgroup of the $R$-symmetry which allows to preserve four supersymmetries. The 3D effective theory exhibits gapped and ungapped phases, which we argue are holographically dual, respectively, to a supersymmetric soliton in AdS$_{5}\times S^{5}$, and a particular quotient of AdS$_5\times S^5$. The gapped phase corresponds to an IR 3D $\mathcal{N}=2$ supersymmetric Yang-Mills-Chern-Simons theory at level $N$, while the ungapped phase is naturally identified with the root of a Higgs branch in the 3D theory. We discuss the extension of the twisting procedure to maximally SUSY Yang-Mills theories in different dimensions, obtaining the relevant duals for 2D and 6D, and comment on the odd dimensional cases. |
| title | Twisted circle compactification of $\mathcal{N}=4$ SYM and its Holographic Dual |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.03739 |