SYM Description of SFT Hamiltonian in a PP-Wave Background

TL;DR

The paper tests and clarifies the holographic map between the light-cone string field theory Hamiltonian in a PP-wave background and the dilatation operator in the BMN sector of N=4 SYM. It corrects the string field theory H3 calculation, derives a unique symmetric, real basis that orthonormalizes the gauge theory inner product, and computes the dilatation matrix to order g2^2; this yields a gauge-theory prediction for order g2^2 string-field theory matrix elements. Remarkably, these predictions agree with recent string-bit Hamiltonian results, reinforcing the proposed holographic correspondence for dynamical, interacting sectors. The work also clarifies basis ambiguities and contrasts the approach with previous proposals, pointing to a deep connection between light-cone SFT and string-bit formalisms and outlining directions for higher-order checks.

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.