Holography for N $$ \mathcal{N} $$ = 1∗ on S 4

Abstract

Abstract:We construct the five-dimensional supergravity dual of the N = 1 * mass deformation of the N = 4 supersymmetric Yang-Mills theory on S 4 and use it to calculate the universal contribution to the corresponding S 4 free energy at large 't Hooft coupling in the planar limit. The holographic RG flow solutions are smooth and preserve four supercharges. As a novel feature compared to the holographic duals of N = 1 * on R 4 , in our backgrounds the five-dimensional dilaton has a non-trivial profile, and the gaugino condensate is fixed in terms of the mass-deformation parameters. Important aspects of the analysis involve characterizing the ambiguities in the partition function of non-conformal N = 1 supersymmetric theories on S 4 as well as the action of S-duality on the N = 1 * theory.

Precision holography for $$ \mathcal{N}={2}^{\ast } $$ on S4 from type IIB supergravity

“…As discussed in [4,11,22] this quantity is scheme dependent. One way to obtain a scheme independent observable is to differentiate (2.7) three times with respect to the dimensionless variable ma, see [11,22] for a more detailed discussion.…”

“…One way to obtain a scheme independent observable is to differentiate (2.7) three times with respect to the dimensionless variable ma, see [11,22] for a more detailed discussion. Another interesting set of physical observables computable by supersymmetric localization is given by Wilson loop operators in various representations of the gauge group.…”

“…It is thus natural to apply these powerful technical results to construct explicit uplifts of other interesting five-dimensional solutions which have found applications in holography. Two particular examples which should be easily accessible are the gravity dual of the N = 1 * cousin of the N = 2 * theory on R 4 [41,42] and S 4 [22].…”

One-loop tests of supersymmetric gauge theories on spheres

“…Nonetheless, certain theories might have further symmetries, opening up the possibility of localizing the theory. A prominent example of this type is the N = 1 * theory where it was shown that one can obtain unambiguous and scheme independent quantities constructed from the partition function [10]. However, there is no known way to localize an N = 1 theory on S 4 .…”

Quantum string test of nonconformal holography

“…Finally, it would be interesting to generalize our calculations to other string solutions in the Pilch-Warner background [4,33,34], to the string dual of the pure N = 2 theory [35,36], where a remarkable match between localization results for Wilson loops and supergravity has been observed [37], and to backgrounds with N = 1 supersymmetry, such as the Polchinski-Strassler background [38] or its S 4 counterpart [39], albeit in this case no fieldtheory predictions are available yet.…”