Green-Schwarz and Pure Spinor Formulations of Chiral Strings

TL;DR

This paper compares Green-Schwarz and pure spinor formulations of chiral superstrings, showing their spectra match RNS models and their tensionless limits describe the same field theories, with new insights into symmetries and vertex operators.

Contribution

It introduces pure spinor formulations of chiral strings using the Oda-Tonin method, revealing hidden symmetries and clarifying the structure of vertex operators.

Findings

Spectra of Green-Schwarz and RNS chiral strings are equivalent.

Tensionless limits correspond to ambitwistor string field theories.

Pure spinor approach uncovers hidden symmetries and simplifies vertex operator construction.

Abstract

Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the Green-Schwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a light-cone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the Oda-Tonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.