SYM Description of SFT Hamiltonian in a PP-Wave Background

TL;DR

This paper establishes a precise correspondence between string field theory Hamiltonian matrix elements and gauge theory dilatation operator matrix elements in a PP-wave background, providing new predictions for higher-order terms.

Contribution

It demonstrates exact agreement between string field theory and gauge theory calculations and predicts higher-order Hamiltonian matrix elements in string field theory.

Findings

Exact match between string field theory and gauge theory results.

Prediction of order g_2^2 Hamiltonian matrix elements in string field theory.

Confirmation of recent string bit model computations.

Abstract

We compute string field theory Hamiltonian matrix elements and compare them with matrix elements of the dilatation operator in gauge theory. We get precise agreement between the string field theory and gauge theory computations once the correct cubic Hamiltonian matrix elements in string field theory and a particular basis of states in gauge theory are used. We proceed to compute the matrix elements of the dilatation operator to order g_2^2 in this same basis. This calculation makes a prediction for string field theory Hamiltonian matrix elements to order g_2^2, which have not yet been computed. However, our gauge theory results precisely match the results of the recent computation by Pearson et al. of the order g_2^2 Hamiltonian matrix elements of the string bit model.