Calculating the Rest Tension for a Polymer of String Bits

TL;DR

This paper applies many-body physics approximation methods to analyze the low energy excitations of a bosonic string bit polymer, deriving an expression for the string's rest tension and evaluating the accuracy of RPA corrections.

Contribution

It introduces a novel application of Hartree-Fock and RPA methods to string bit models, deriving an exact relation for string tension and assessing RPA accuracy with large correction analysis.

Findings

Derived an exact relation between string tension and correlation functions.

Calculated large first-order RPA corrections (~15%) for a specific potential.

Assessed the accuracy of RPA and proposed a summation method for large terms.

Abstract

We explore the application of approximation schemes from many body physics, including the Hartree-Fock method and random phase approximation (RPA), to the problem of analyzing the low energy excitations of a polymer chain made up of bosonic string bits. We accordingly obtain an expression for the rest tension $T_0$ of the bosonic relativistic string in terms of the parameters characterizing the microscopic string bit dynamics. We first derive an exact connection between the string tension and a certain correlation function of the many-body string bit system. This connection is made for an arbitrary interaction potential between string bits and relies on an exact dipole sum rule. We then review an earlier calculation by Goldstone of the low energy excitations of a polymer chain using RPA. We assess the accuracy of the RPA by calculating the first order corrections. For this purpose we specialize to the unique scale invariant potential, namely an attractive delta function potential in two (transverse) dimensions. We find that the corrections are large, and discuss a method for summing the large terms. The corrections to this improved RPA are roughly 15\%.