$\mathcal{N}=2$ Super Yang-Mills in AdS$_4$ and $F_{\text{AdS}}$-maximization
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| Format: | Preprint |
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2025
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| _version_ | 1866918056223047680 |
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| author | Bason, Davide Copetti, Christian Di Pietro, Lorenzo Ji, Ziming |
| author_facet | Bason, Davide Copetti, Christian Di Pietro, Lorenzo Ji, Ziming |
| contents | We investigate the dynamics of four-dimensional $\mathcal{N}=2$ $SU(2)$ super Yang--Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function $F_{\text{AdS}}=-\log Z_{\text{AdS}}$. At weak coupling $ΛL \ll 1$ the maximization singles out the Dirichlet boundary condition with an $SU(2)$ boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for $ΛL \sim \mathcal{O}(1)$ new boundary conditions are favored, with gauge-group higgsed down to $U(1)$, matching the expectation from the flat space limit. We use supersymmetric localization to compute $Z_{\text{AdS}}$ nonperturbatively. We further provide evidence for a relation between $F_{\text{AdS}}$ and the $\mathcal{N}=2$ prepotential in AdS background. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_05162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{N}=2$ Super Yang-Mills in AdS$_4$ and $F_{\text{AdS}}$-maximization Bason, Davide Copetti, Christian Di Pietro, Lorenzo Ji, Ziming High Energy Physics - Theory We investigate the dynamics of four-dimensional $\mathcal{N}=2$ $SU(2)$ super Yang--Mills theory on an AdS background. We propose that the boundary conditions that preserve the AdS super-isometries are determined by maximizing the real part of the AdS partition function $F_{\text{AdS}}=-\log Z_{\text{AdS}}$. At weak coupling $ΛL \ll 1$ the maximization singles out the Dirichlet boundary condition with an $SU(2)$ boundary global symmetry, corresponding to the classical vacuum at the origin of the Coulomb branch with fully un-higgsed gauge group. We find that for $ΛL \sim \mathcal{O}(1)$ new boundary conditions are favored, with gauge-group higgsed down to $U(1)$, matching the expectation from the flat space limit. We use supersymmetric localization to compute $Z_{\text{AdS}}$ nonperturbatively. We further provide evidence for a relation between $F_{\text{AdS}}$ and the $\mathcal{N}=2$ prepotential in AdS background. |
| title | $\mathcal{N}=2$ Super Yang-Mills in AdS$_4$ and $F_{\text{AdS}}$-maximization |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.05162 |