Rotating particles in AdS: Holography at weak gauge coupling and without conformal symmetry

TL;DR

This paper explores the gauge/gravity duality for maximally supersymmetric Yang-Mills theory in various dimensions, extending previous results to operators with angular momentum in AdS, and demonstrates the correspondence at zero gauge coupling.

Contribution

It extends the holographic correspondence to operators with angular momentum in AdS and connects string solutions to gauge theory correlators without conformal symmetry.

Findings

Reproduces free-field gauge theory results from string theory.

Shows the spinning string solutions relate to boundary points in Euclidean AdS.

Demonstrates the duality at zero gauge coupling ignoring string interactions.

Abstract

We consider gauge/gravity correspondence between maximally supersymmetric Yang-Mills theory in ($p+1$) dimensions and superstring theory on the near-horizon limit of the D$p$-brane solution. The string-frame metric is AdS$_{p+1}\times S^{8-p}$ times a Weyl factor, and there is no conformal symmetry except for $p=3$. In a previous paper by one of the present authors, the free-field result of gauge theory has been reproduced from string theory for a particular operator which has angular momentum along $S^{8-p}$. In this paper, we extend this result to operators which have angular momenta along AdS$_{p+2}$. Our approach is based on a Euclidean formulation proposed by Dobashi, Shimada and Yoneya and on the "string bit" picture. We first show that the spinning string solution in Lorentzian AdS, found by Gubser, Klebanov and Polyakov, can be recast in a form which connects two points on the boundary of Euclidean AdS. Transition amplitudes of such strings can be interpreted as gauge theory correlators. We study the case of zero gauge coupling by ignoring interactions among string bits (massless particles in ten-dimensional spacetime which constitute a string), and show that the free-field results of gauge theory are reproduced.