A Formula for Multi-Loop 4-Particle Amplitude in Superstring Theory

TL;DR

This paper proposes an explicit formula for multi-loop 4-particle amplitudes in superstring theory, demonstrating modular invariance and factorization, which suggests the theory's finiteness and simplicity.

Contribution

It introduces a new explicit formula for arbitrary loop 4-particle amplitudes in superstring theory, validated by key consistency tests.

Findings

The formula passes modular invariance test.

The formula satisfies factorization properties.

Supports superstring theory's finiteness and simplicity.

Abstract

Based on the recent developments of explicit computations at 2 loops in superstring theory in the covariant RNS formalism, we propose an explicit formula for the arbitrary loop 4-particle amplitude in superstring theory. We prove that this formula passes two very difficult tests: modular invariance and factorization. If proved, this shows that superstring theory is not only finite order by order in perturbation theory but is also exceptionally simple.