Simplifying one-loop amplitudes in superstring theory

TL;DR

This paper simplifies and analyzes one-loop 4-point vector boson amplitudes in superstring theory, confirming supersymmetry Ward identities and exploring their IR/UV behavior, revealing unexpected features like absence of massless poles.

Contribution

It provides a simplified expression for superstring one-loop amplitudes in N=1 supersymmetric configurations and compares different formalisms, highlighting challenges in unifying approaches.

Findings

Amplitudes vanish for non-MHV configurations, confirming supersymmetry.

Simplified expressions for MHV amplitudes are derived.

Unexpected absence of massless poles at generic modular parameters.

Abstract

We show that 4-point vector boson one-loop amplitudes, computed in ref.[1] in the RNS formalism, around vacuum configurations with open unoriented strings, preserving at least N=1 SUSY in D=4, satisfy the correct supersymmetry Ward identities, in that they vanish for non MHV configurations (++++) and (-+++). In the MHV case (--++) we drastically simplify their expressions. We then study factorisation and the limiting IR and UV behaviour and find some unexpected results. In particular no massless poles are exposed at generic values of the modular parameter. Relying on the supersymmetric properties of our bosonic amplitudes, we extend them to manifestly supersymmetric super-amplitudes and compare our results with those obtained in the D=4 hybrid formalism, pointing out difficulties in reconciling the two approaches for contributions from N=1,2 sectors.