A general BRST approach to string theories with zeta function regularizations

TL;DR

This paper introduces a novel BRST approach for string theories using zeta function regularization to handle divergences, enabling rigorous analysis of various string models including tensionless and conformal tensionless strings.

Contribution

It presents a general BRST framework with zeta function regularization applicable to diverse string models, offering a more rigorous and unified analysis method.

Findings

Rederived known results in a new, more rigorous way

Discovered a new solution for the conformal tensionless string in four dimensions

Provided insights into different state space representations for string models

Abstract

We propose a new general BRST approach to string and string-like theories which have a wider range of applicability than e g the conventional conformal field theory method. The method involves a simple general regularization of all basic commutators which makes all divergent sums to be expressible in terms of zeta functions from which finite values then may be extracted in a rigorous manner. The method is particular useful in order to investigate possible state space representations to a given model. The method is applied to three string models: The ordinary bosonic string, the tensionless string and the conformal tensionless string. We also investigate different state spaces for these models. The tensionless string models are treated in details. Although we mostly rederive known results they appear in a new fashion which deepens our understanding of these models. Furthermore, we believe that our treatment is more rigorous than most of the previous ones. In the case of the conformal tensionless string we find a new solution for d=4.