The Four-Point Function on a Surface of Infinite Genus

TL;DR

This paper evaluates the four-point string scattering amplitude on an infinite-genus surface, revealing its divergence structure and implications for the universal moduli space approach in string theory.

Contribution

It provides the first detailed analysis of the four-point function on an infinite-genus surface, showing that no new divergences arise from the infinite handles.

Findings

Amplitude has poles for physical states

Divergences occur at moduli space boundary

No new divergences from infinite handles

Abstract

The four-point function arising in the scattering of closed bosonic strings in their tachyonic ground state is evaluated on a surface of infinite genus. The amplitude has poles corresponding to physical intermediate states and divergences at the boundary of moduli space, but no new types of divergences result from the infinite number of handles. The implications for the universal moduli space approach are briefly discussed.