The Heterotic Green-Schwarz Superstring on an N=(2,0) Super-Worldsheet

TL;DR

This paper introduces a novel formulation of the heterotic Green-Schwarz superstring on an N=(2,0) super-worldsheet, simplifying the calculation of scattering amplitudes and resolving issues present in previous formalisms.

Contribution

It defines the superstring action on an N=(2,0) super-worldsheet, enabling gauge fixing to a free-field action and facilitating amplitude calculations similar to light-cone methods.

Findings

Elimination of interaction-point operators in the light-cone approach.

Gauge-fixed covariant action is non-anomalous and superconformally invariant.

Scattering amplitudes resemble those from the light-cone approach.

Abstract

By defining the heterotic Green-Schwarz superstring action on an N=(2,0) super-worldsheet, rather than on an ordinary worldsheet, many problems with the interacting Green-Schwarz superstring formalism can be solved. In the light-cone approach, superconformally transforming the light-cone super-worldsheet onto an N=(2,0) super-Riemann surface allows the elimination of the non-trivial interaction-point operators that complicate the evaluation of scattering amplitudes. In the Polyakov approach, the ten-dimensional heterotic Green-Schwarz covariant action defined on an N=(2,0) super-worldsheet can be gauge-fixed to a free-field action with non-anomalous N=(2,0) superconformal invariance, and integrating the exponential of the covariant action over all punctured N=(2,0) super-Riemann surfaces produces scattering amplitudes that closely resemble amplitudes obtained using the unitary light-cone approach.