Fermionic one-loop amplitudes of the RNS superstring

Understand

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.