Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory

Abstract

$\mathcal{N}=4$ 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 $U(N)$ $\mathcal{N}=4$ 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 term at large $N$ in the supergravity and localization results agree exactly as a function of the t' Hooft coupling $\lambda$.

Reference added; minor typos corrected in Section 2.2 and equations (3.13), (3.14), (3.21), (3.23); terms rearranged in equation (4.19)

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Cited by in corpus (2)

• AdS/BCFT with Brane-Localized Scalar Field
• Mapping out the internal space in AdS/BCFT with Wilson loops