Supersymmetric Yang-Mills, Spherical Branes, and Precision Holography

Abstract

Using supersymmetric localization we compute the free energy and BPS Wilson loop vacuum expectation values for planar maximally supersymmetric Yang-Mills theory on $S^d$ in the strong coupling limit for $2\le d<6$. The same calculation can also be performed in supergravity using the recently found spherical brane solutions. We find excellent agreement between the two sets of results. This constitutes a non-trivial precision test of holography in a non-conformal setting. The free energy of maximal SYM on $S^6$ diverges in the strong coupling limit which might signify the onset of little string theory. We show how this divergence can be regularized both in QFT and in supergravity. We also consider $d=7$ with a small negative 't Hooft coupling and show that the free energy and Wilson loop vacuum expectation value agree with the results from supergravity after addressing some subtleties.

arXiv comment58 pages

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• dS Spaces and Brane Worlds in Exotic String Theories
• Supersymmetric domain walls in maximal 6D gauged supergravity I
• Seven-dimensional super Yang-Mills at negative coupling
• Wilson Loops and Spherical Branes
• Five-dimensional gauge theories on spheres with negative couplings
• Supersymmetric domain walls in maximal 6D gauged supergravity II
• Supersymmetric domain walls in maximal 6D gauged supergravity III
• Partition functions on squashed seven-spheres and holography
• Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms