Ultraviolet Limit of Open String Theory

TL;DR

This paper demonstrates that perturbative infrared finiteness in string theory implies perturbative ultraviolet finiteness, using mathematical techniques applicable to both open and closed strings, and introduces a natural world-sheet ultraviolet regulator.

Contribution

It provides a novel derivation linking infrared and ultraviolet finiteness in string theory, independent of modular invariance and supersymmetry, based on the asymptotics of the Selberg trace formula.

Findings

Infrared finite string theories are also ultraviolet finite.

A natural world-sheet ultraviolet regulator is identified.

The approach applies to both open and closed string amplitudes.

Abstract

We confirm the intuition that a string theory which is perturbatively infrared finite is automatically perturbatively ultraviolet finite. Our derivation based on the asymptotics of the Selberg trace formula for the Greens function on a Riemann surface holds for both open and closed string amplitudes and is independent of modular invariance and supersymmetry. The mass scale for the open strings stretched between Dbranes suggests a natural world-sheet ultraviolet regulator in the string path integral, preserving both T-duality and open-closed string world-sheet duality. Note added (Jan 2005): Comments and related references added.