Supersymmetry Breaking Effects using the Pure Spinor Formalism of the Superstring

TL;DR

This paper computes supersymmetry-breaking effects in heterotic superstrings on Calabi-Yau manifolds using the pure spinor formalism, highlighting subtleties in loop amplitude calculations similar to those in the RNS formalism.

Contribution

It demonstrates how to calculate supersymmetry-breaking amplitudes in the pure spinor formalism and discusses related subtleties in the regularization process.

Findings

Pure spinor formalism reproduces known supersymmetry-breaking effects.

Loop amplitude calculations involve subtleties similar to RNS formalism.

Regularization issues impact amplitude computations in pure spinor approach.

Abstract

The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously break supersymmetry at one-loop order even when it is unbroken at tree-level. It is known that calculating the supersymmetry-breaking effects in this model gives a relatively accessible test case of the subtleties of superstring perturbation theory in the RNS formalism. In the present paper, we calculate the relevant amplitudes in the pure spinor approach to superstring perturbation theory, and show that the regulator used in computing loop amplitudes in the pure spinor formalism leads to subtleties somewhat analogous to the more familiar subtleties of the RNS approach.