A Calculation of the plane wave string Hamiltonian from N=4 super-Yang-Mills theory

TL;DR

This paper demonstrates how to compute the string theory Hamiltonian matrix elements from N=4 super-Yang-Mills theory, revealing a modified state-operator map necessary for agreement at nonzero string coupling.

Contribution

It identifies the operator dual to the string Hamiltonian at finite coupling and explicitly constructs the modified state-operator map in gauge theory.

Findings

Matrix elements match string theory predictions with the modified map.

Constructed the explicit form of the new state-operator map.

Calculated anomalous dimensions of operators at nonzero coupling.

Abstract

Berenstein, Maldacena, and Nastase have proposed, as a limit of the strong form of the AdS/CFT correspondence, that string theory in a particular plane wave background is dual to a certain subset of operators in the N=4 super-Yang-Mills theory. Even though this is a priori a strong/weak coupling duality, the matrix elements of the string theory Hamiltonian, when expressed in gauge theory variables, are analytic in the 't Hooft coupling constant. This allows one to conjecture that, like the masses of excited string states, these can be recovered using perturbation theory in Yang-Mills theory. In this paper we identify the difference between the generator of scale transformations and a particular U(1) R-symmetry generator as the operator dual to the string theory Hamiltonian for nonvanishing string coupling. We compute its matrix elements and find that they agree with the string theory prediction provided that the state-operator map is modified for nonvanishing string coupling. We construct this map explicitly and calculate the anomalous dimensions of the new operators. We identify the component arising from the modification of the state-operator map with the contribution of the string theory contact terms to the masses of string states.