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

Abstract

We find a new supersymmetric solution of type IIB supergravity which is holographically dual to the planar limit of the four-dimensional N = 2 * supersymmetric Yang-Mills theory on S 4 . We study a probe fundamental string in this background which is dual to a supersymmetric Wilson loop in the N = 2 * theory. Using holography we calculate the expectation value of this line operator to leading order in the 't Hooft coupling. The result is a non-trivial function of the mass parameter of the N = 2 * theory that precisely matches the result from supersymmetric localization.

Supersymmetric Yang-Mills, spherical branes, and precision holography

“…Given any satisfying (2.3) we can define a vector field v M ≡ Γ M that automatically satisfies v M v M = 0. We then choose so that v 0 = 1, v 8,9 = v i = 0, and along one particular equator of the sphere v µ v µ = 1. We will later take the large N limit where it is assumed that instantons can be ignored [2,7].…”

“…This on-shell string action diverges close to the UV boundary of the supergravity solution and we have to renormalize it using appropriate covariant counterterms built out of the tendimensional supergravity fields. This leads to the standard counterterm commonly used to regularize string on-shell actions [9,32]. In terms of the gauged supergravity fields, this counterterm takes the form…”

“…The free energy and the Wilson line VEV for N = 4 can also be computed holographically using standard results in the literature. An efficient way to obtain the end result on S 4 is to take the m = 0 limit of the N = 2 * calculations in [7] and [9]. 11 4.4 D4-branes…”

“…Indeed this was pursued extensively and many important developments are summarized in [1]. These two examples also offer the possibility to break conformal invariance and part of the supersymmetry while still maintaining calculational control both in the field theory [2,3,4,5] and the supergravity side [6,7,8,9,10]. This collection of results provides a non-trivial precision test of holography away from the conformal limit.…”

Holographic RG flows in $$N=4$$ N = 4 SCFTs from half-maximal gauged supergravity

“…The uplifted solutions would be desirable for a full holographic study of N = 4 CSM theories. This should provide an analogue of the recent uplifts of the GPPZ flow describing a massive deformation of N = 4 SYM [38,39]. The embedding of the non-compact gauge groups SO(3, 1) × SO (3,1) and SO(4) × SO(3, 1) would also be worth considering.…”