Fermionic one-loop amplitudes of the RNS superstring

TL;DR

This paper computes massless one-loop amplitudes with fermions in the open RNS superstring, introducing new techniques for spin structure summation and expressing results with elliptic functions, advancing string amplitude calculations.

Contribution

It develops methods to evaluate and sum fermionic correlators over spin structures, generalizing Riemann identities and connecting to elliptic multiple zeta values.

Findings

Derived explicit worldsheet integrands for fermionic one-loop amplitudes.

Introduced techniques for spin structure summation using generalized Riemann identities.

Expressed results in terms of elliptic functions related to multiple zeta values.

Abstract

We investigate massless n-point one-loop amplitudes of the open RNS superstring with two external fermions and determine their worldsheet integrands. The contributing correlation functions involving spin-1/2 and spin-3/2 operators from the fermion vertices are evaluated to any multiplicity. Moreover, we introduce techniques to sum these correlators over the spin structures of the worldsheet fermions such as to manifest all cancellations due to spacetime supersymmetry. These spin sums require generalizations of the Riemann identities among Jacobi theta functions, and the results can be expressed in terms of doubly-periodic functions known from the mathematics literature on elliptic multiple zeta values. On the boundary of moduli space, our spin-summed correlators specialize to compact representations of fermionic one-loop integrands for ambitwistor strings.