Two-Point Superstring Tree Amplitudes Using the Pure Spinor Formalism

TL;DR

This paper develops a method within the pure spinor formalism to compute finite two-point tree amplitudes in superstring theory, confirming their consistency with field theory results and extending previous bosonic string findings.

Contribution

It introduces a prescription for calculating two-point superstring amplitudes in the pure spinor formalism, verifying their finiteness and agreement with field theory, and generalizes earlier bosonic string results.

Findings

Two-point amplitudes are finite and match field theory expressions.

The method is verified for superstrings using a BRST exact operator.

Results extend previous bosonic string amplitude calculations.

Abstract

We provide a prescription for computing two-point tree amplitudes in the pure spinor formalism that are finite and agree with the corresponding expression in the field theories. In [arXiv:1906.06051v1-arXiv:1909.03672v3], same results were presented for bosonic strings and it was mentioned they can be generalized to superstrings. The pure spinor formalism is a successful super-Poincare covariant approach to quantization of superstrings [arXiv:hep-th/0001035v2]. Because the pure spinor formalism is equivalent to other superstring formalisms, we explicitly verify the above claim. We introduce a mostly BRST exact operator in order to achieve this.