String Corrections to the Holographic RG Flow of Supersymmetric SU(N) x SU(N+M) Gauge Theory

TL;DR

This paper investigates string corrections to the holographic RG flow of a supersymmetric SU(N) x SU(N+M) gauge theory, showing how these corrections align with field theory predictions and affect operator anomalous dimensions.

Contribution

It identifies specific higher-derivative terms in the string effective action relevant to the RG flow and demonstrates their impact on matching supergravity solutions with field theory beta functions.

Findings

String corrections include specific R^3(H_3)^2 and R^3(F_3)^2 terms.

These corrections are comparable in magnitude to R^4 terms in the effective action.

Corrected supergravity fields match the RG flow and beta functions of the dual gauge theory.

Abstract

We study leading string corrections to the type IIB supergravity solution dual to the ${\cal N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory coupled to bifundamental chiral superfields $A_i, B_j$, $i,j=1,2$. This solution was found in hep-th/0007191, and its asymptotic form describing logarithmic RG flow was constructed in hep-th/0002159. The leading tree-level string correction to the type IIB string effective action is represented by the invariant of the form $\a'{}^3 (R^4 + ...)$. Since the background contains 3-form field strengths, we need to know parts of this invariant that depend on them. By analyzing the 5-point superstring scattering amplitudes we show that only a few specific $R^3 (H_3)^2$ and $R^3 (F_3)^2$ terms are present in the effective action. Their contribution to the holographic RG flow turns out to be of the same order as of the $R^4$ terms. Using this fact we show that it is possible to have agreement between the $\alpha'$-corrected radial dependence of the supergravity fields and the RG flow dictated by the NSVZ beta functions in field theory. The agreement with field theory requires that the anomalous dimension of the operators $\Tr (A_i B_j)$ is corrected by a term of order $(M/N)^4 \lambda^{-1/2}$ from its value $-{1 \over 2} $ found for M=0 ($\lambda$ is the appropriate 't Hooft coupling which is assumed to be strong).