On BPS Strings in ${\mathcal N}=4$ Yang-Mills Theory

TL;DR

This paper investigates singular BPS string-like defects in the abelian sector of ${\mathcal N}=4$ super Yang-Mills theory, exploring their geometric description, holographic duals, and regularization methods to understand their physical properties.

Contribution

It introduces a geometric framework for BPS strings as zeros of holomorphic functions, maps them to surface operators, and establishes their holographic duals as probe D3-branes in $AdS_5\times S^5$ with a regularization scheme for finite charges.

Findings

BPS strings correspond to intersections of holomorphic zeros with $S^3$.

String defects are dual to noncompact probe D3-branes in $AdS_5\times S^5$.

A regularization scheme yields finite energy and charges.

Abstract

We study singular time-dependent $\frac{1}{8}$-BPS configurations in the abelian sector of ${{\mathcal N}= 4}$ supersymmetric Yang-Mills theory that represent BPS string-like defects in ${{\mathbb R}\times S^3}$ spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to $\frac{1}{8}$-BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global $AdS_5\times S^5$ that share supersymmetries with a class of dual-giant gravitons. For simple configurations, we demonstrate how to define a good variational problem and propose a regularization scheme that leads to finite energy and global charges on both sides of the holographic correspondence.