Closed String Self-energy on the Lightcone Worldsheet Lattice

TL;DR

This paper investigates the one-loop self-energy correction for closed bosonic strings on a discretized lightcone worldsheet lattice, demonstrating divergence cancellation via counterterms and a regularization scheme consistent with Lorentz invariance.

Contribution

It introduces a numerical approach to evaluate string self-energy corrections on a lattice, assessing the lattice's effectiveness as a divergence regulator in string perturbation theory.

Findings

Divergences are cancelable by area counterterms and slope renormalization.

Residual finite parts align with Lorentz invariance under a new regularization.

The lattice discretization effectively evaluates moduli integrals numerically.

Abstract

We study the one loop correction to the closed bosonic string propagator, including the possibile presence of D-branes, by discretizing the light cone worldsheet on an M times N rectangular lattice, with M proportional to P^+ and N+1 proportional to ix^+. The integrals over the moduli then become sums which we evaluate numerically. The main purpose of this study is to assess the reliability of the worldsheet lattice as a regulator of the divergences in string perturbation theory. There are two natural geometrical counterterms for the lightcone worldsheet, one proportional to the area of the worldsheet and the other proportional to the length of worldsheet boundaries, tracing the ends of open strings. We show that the divergences in the closed string self-energy can be cancelled by the area counterterm and a renormalization of the Regge slope parameter. The residual finite part is compatible with Lorentz invariance, provided a novel regularization, natural to the lightcone worldsheet lattice and described in this article, is employed.