Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

TL;DR

This paper explores the AdS/CFT correspondence by modeling heavy quarks with macroscopic strings, analyzing their dynamics, boundary conditions, and potential, revealing nonanalytic behavior and geometric dualities at strong coupling.

Contribution

It introduces macroscopic strings as heavy quark probes in AdS/CFT, studies their dynamics and boundary conditions, and predicts nonanalytic quark-antiquark potentials at strong coupling.

Findings

Quark-antiquark potential exhibits a square-root branch cut nonanalyticity.

Boundary conditions for macroscopic strings match supergravity predictions.

Geometric duality explains emergence of AdS geometry from gauge theory.

Abstract

We study some aspects of Maldacena's large $N$ correspondence between N=4 superconformal gauge theory on D3-brane and maximal supergravity on AdS_5xS_5 by introducing macroscopic strings as heavy (anti)-quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on D3-brane world-volume. We first study deformation and fluctuation of D3-brane when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for macroscopic string in anti-de Sitter supergravity. As by-product we clarify how Polchinski's Dirichlet / Neumann open string boundary conditions arise dynamically. We then study non-BPS macroscopic string anti-string pair configuration as physical realization of heavy quark Wilson loop. We obtain quark-antiquark static potential from the supergravity side and find that the potential exhibits nonanalyticity of square-root branch cut in `t Hooft coupling parameter. We put forward the nonanalyticity as prediction for large-N gauge theory at strong `t Hooft coupling limit. By turning on Ramond-Ramond zero-form potential, we also study theta-vacuum angle dependence of the static potential. We finally discuss possible dynamical realization of heavy N-prong string junction and of large-N loop equation via local electric field and string recoil thereof. Throughout comparisons of the AdS-CFT correspondence, we find crucial role played by `geometric duality' between UV and IR scales on directions perpendicular to D3-brane and parallel ones, explaining how AdS5 spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.