PP-Wave Holography for Dp-Brane Backgrounds

TL;DR

This paper explores the holographic relationship between string theories in Dp-brane backgrounds and supersymmetric gauge theories, using a tunneling approach to analyze two-point functions and infra-red behaviors for various p.

Contribution

It develops a method to extract two-point functions in time-dependent backgrounds and applies it to D0-branes, extending holography to non-conformal Dp-brane cases.

Findings

Two-point functions for D0-branes match previous supergravity results.

Infra-red behaviors indicate nontrivial fixed points in dual gauge theories.

Time-dependent backgrounds are successfully analyzed for p ≠ 3, p < 5.

Abstract

As an extension of the so-called BMN conjecture, we investigate the plane-wave limit for possible holographic connection between bulk string theories in non-conformal backgrounds of D$p$-branes and the corresponding supersymmetric gauge theories for $p<5$. Our work is based on the tunneling picture for dominant null trajectories of strings in the limit of large angular momentum. The tunneling null trajectories start from the near-horizon boundary and return to the boundary, and the resulting backgrounds are time-dependent for general D$p$-branes except for $p=3$. We develop a general method for extracting diagonalized two-point functions for boundary theories as Euclidean (bulk) S-matrix in the time-dependent backgrounds. For the case of D0-brane, two-point functions of supergravity modes are shown to agree with the results derived previously by the perturbative analysis of supergravity. We then discuss the implications of the holography for general cases of D$p$-branes including the stringy excitations. All the cases ($p\ne 3, p<5$) exhibit interesting infra-red behaviors, which are different from free-field theories, suggesting the existence of quite nontrivial fixed-points in dual gauge theories.