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 ≤ 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 nonconformal 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.

Five-dimensional gauge theories on spheres with negative couplings

“…which is half the 7d large separation kernel with 16 supersymmetries [18]. Hence we expect the eigenvalues to behave similarly to that case.…”

“…1 For particular expressions in 5d case see [15][16][17]. 2 We use the conventions for g 2 YM in [18].…”

“…Hence the approximation in (2.8) is valid if λ −1 eff −1. In addition, we can borrow from the 7d result in [18] to show that here the free energy in this limit is…”

“…We can also give a large mass to the antisymmetric hypermultiplet. In this case the effective coupling is given by 18) and the saddle point equation for the matrix integral turns into…”

dS spaces and brane worlds in exotic string theories

“…On the same note, in[31,32] the authors argued that time dependent backgrounds might circumvent the dS swampland conjecture.2 Questions concerning the backreaction of spherical Euclidean D-branes have been studied lately in a series of papers[37,38].…”