Holography of BPS surface operators

TL;DR

Koh and Yamaguchi analyze dilatation-invariant BPS surface operators in ${\\cal N}=4$ SYM and their type IIB holographic duals on ${\\rm AdS}_5 \times S^5$. They first study a concrete 1/4 BPS gauge-theory surface operator with a scalar profile $${\\Phi} \\sim \\beta/\\sqrt{z^1 z^2}$$, including holonomy-induced monodromy cancellation, then propose a D3-brane probe wrapping a holomorphic 4-cycle in the gravity dual, and verify supersymmetry, vacuum expectation value, and correlation functions with chiral primaries, finding agreement in leading order and informative next-to-leading corrections. The work then generalizes to a broad class of dilatation-invariant, less-BPS surface operators defined by homogeneous algebraic equations, outlining their gravity duals as holomorphic D3-brane embeddings and providing several concrete examples (1/2, 1/4, 1/8 BPS). Overall, the paper demonstrates a consistent gauge/gravity correspondence for surface operators across multiple BPS levels and lays groundwork for including backreaction and studying other SCFTs. The results illuminate how large-charge/large-parameter limits control gravity/gauge-theory expansions and suggest further avenues for computing correlators and exploring anomalies in curved or generalized setups.

Abstract

We study a class of dilatation invariant BPS surface operators in 4-dimensional N=4 Super Yang-Mills theory and their holographic duals in type IIB string theory in AdS_5 x S^5. First we take an example of 1/4 BPS surface operator and study it in detail from the holographic point of view. The gravity dual of this surface operator is a D3-brane characterized by a holomorphic submanifold. The supersymmetry and vacuum expectation value are checked in both the gauge theory side and the gravity side. We also calculate the correlation functions with the chiral primary operators in both sides and find good agreement. Next we consider more general dilatation invariant BPS surface operators. The gravity duals of those operators are proposed.

Figures (1)

• Figure 1: The patches of the coordinates. We introduce two patches (1) $0<\phi_1<2\pi$, and (2) $-\pi<\phi_1<\pi$. They are connected by the gauge transformation with the identity matrix in (a) $0<\phi_1<\pi$ and the matrix $g$ in (b) $-\pi<\phi_1<0$.