PP-wave string interactions from perturbative Yang-Mills theory

TL;DR

This paper investigates the BMN limit of N=4 SYM and its dual IIB pp-wave string theory, identifying a perturbative framework with two key parameters: the effective gauge coupling $\lambda' = g_{YM}^2 N/J^2$ and the genus-counting parameter $g_2^2=J^4/N^2$. It shows that string interactions correspond to higher-genus YM correlators, with the physical string coupling given by $g_2\sqrt{\lambda'}$, and provides explicit calculations of torus (genus-one) corrections to BMN operator dimensions as mass renormalizations, matching second-order perturbation theory using YM-derived three-point data. The authors propose a concrete dictionary between YM three-point functions and light-cone string field theory amplitudes, and perform nontrivial consistency checks, including a unitarity check and a comparison with the delta-functional overlap in string field theory. The results offer a clear, computable realization of gauge–string duality in a regime where both sides are perturbative, enabling precise tests of the pp-wave/CFT correspondence and guiding future extensions to broader operator content and finite μ.

Abstract

Recently, Berenstein et al. have proposed a duality between a sector of N=4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be lambda'=g_{YM}^2 N/J^2=1/(mu p^+ alpha')^2. We study Yang-Mills theory at small lambda' (large mu) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g_2^2=J^4/N^2=(4 pi g_s)^2 (mu p^+ alpha')^4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g_2 sqrt{lambda'} as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g_2^2 and lambda' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our earlier computation.

Theorems & Definitions (6)

• Lemma C.1
• Proposition C.2
• Proposition C.3
• Theorem C.4
• Theorem C.5
• Lemma C.6