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Localizing gauge theories on $S^d$

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arxiv 1512.06924 v2 pith:NQURKITJ submitted 2015-12-22 hep-th

Joseph A. Minahan This is my paper · ORCID
classification hep-th
keywords gaugesupersymmetrictheorieslocalizedmaximallyyang-millsactionargue
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abstract

We conjecture the form of the one-loop determinants for localized gauge theories with eight supersymmetries on $d$-dimensional spheres. Combining this with results for the localized action, we investigate the strong coupling behavior in the large $N$ limit for a continuous range of $d$. In particular, we find the $N$ dependence of the free energy for supersymmetric Yang-Mills with only a vector multiplet in $3<d<4$ and for maximally supersymmetric Yang-Mills in $3< d<6$. We also argue that this gives an effective way to regularize divergences after localization in $d=4$ for ${\mathcal N}=2$ gauge theories and $d=6$ for the maximally supersymmetric case.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Two-point functions in $4-2\,\varepsilon$ dimensions from localization

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    Localization yields all-loop leading-ε results for two-point functions in 4-2ε SYM that agree with flat-space perturbation at O(ε) and motivate a conjecture for the dimension-two operator at O(ε²).

  2. $F$-extremization determines certain large-$N$ CFTs

    hep-th 2024-12 conditional novelty 7.0 of 10

    Melonic large-N CFTs are exactly the conformal mean field theories that extremize the universal part of the sphere free energy under linear IR marginality constraints.

  3. Monodromy Defects in Maximally Supersymmetric Yang-Mills Theories from Holography

    hep-th 2025-12 conditional novelty 6.0 of 10

    Codimension-2 monodromy defects in p=2,3,4 maximal SYM are realized by re-interpreting spindle solutions, and their defect entanglement entropy is shown to be proportional to the ambient free energy.

  4. Tracing Transcendentality in Protected Correlators of N=4 SYM

    hep-th 2026-06 unverdicted novelty 5.0 of 10

    Explicit two-loop computations of protected correlators in N=4 SYM yield a universal one-loop term and a planar extrapolation at arbitrary dimension controlled by stress-tensor multiplet count.

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