Holographic and localization calculations of boundary F for N=4 SUSY Yang-Mills theory

N = 4 Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called boundary F, conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary F for U(N) N = 4 SYM theory with the most general half-supersymmetric boundary conditions arising from string theory constructions with D3-branes ending on collections of D5-branes and/or NS5-branes. We first perform the calculation holographically by evaluating the entanglement entropy for a half-ball centered on the boundary using the Ryu-Takayanagi formula in the dual type IIB supergravity solutions. For boundary conditions associated with D3-branes ending on D5 branes only or NS5-branes only, we also calculate boundary F exactly by evaluating the hemisphere partition function using supersymmetric localization. The leading terms at large N in the supergravity and localization results agree exactly as a function of the t' Hooft coupling lambda.

Automated summary

In this paper, the authors studied the properties of U(N) N = 4 SYM theory under specific boundary conditions, showing that boundary F decreases under boundary renormalization group flows, and the leading terms at large N in the supergravity and localization results agree.