Evidence for Gauge/Gravity Correspondence for D$p$-branes at Weak 't Hooft Coupling

TL;DR

This paper demonstrates that the free-field two-point functions in Dp-brane gauge theories at weak 't Hooft coupling can be derived from string theory, extending gauge/gravity correspondence insights to weak coupling regimes.

Contribution

It provides a novel derivation of free-field two-point functions from string theory for Dp-branes at weak coupling, bridging a gap in gauge/gravity duality understanding.

Findings

Reproduces free-field two-point functions from string theory

Shows independence of string bits at zero tension

Extends gauge/gravity correspondence to weak coupling

Abstract

We consider gauge/gravity correspondence for general Dp-branes with $0\le p\le 4$, namely, the duality between the (p+1)-dimensional maximally supersymmetric Yang-Mills theory and superstring theory on the near-horizon limit of the Dp-brane solution. It has been known that in the large N gauge theory at zero temperature and strong 't Hooft coupling, the two-point functions of operators corresponding to supergravity modes obey power-law, with a power different from the free-field value when $p\neq 3$. In this work, we show that the free-field result of gauge theory can be reproduced from the bulk string theory, for the two-point function of an operator Tr(Z^J), where Z is a complex combination of two scalar fields. We assume the spatial direction of worldsheet is discretized into J bits, and use the fact that these bits become independent particles when string tension is zero.