The one loop measure in the Group Theoretic approach to String Theory: the case of two finite fixed points

TL;DR

This paper computes the one-loop scattering measure for bosonic strings using a group theoretic approach, focusing on cases with two finite fixed points and a multiplier, advancing the understanding of string interactions.

Contribution

It introduces a method to calculate the one-loop measure in string theory using projective transformations characterized by two fixed points and a multiplier.

Findings

Derived explicit expressions for the measure in the two fixed points case.

Enhanced the group theoretic framework for string loop calculations.

Provided insights into the structure of string scattering amplitudes.

Abstract

The measure for the one loop scattering of one and $N$ bosonic strings is calculated using the Group Theoretic approach to String Theory. The calculation is done for the case when the projective transformation associated with the loop can be parametrized in terms of two finite fixed points and the multiplier.