Spin fields for the spinning particle

TL;DR

This paper introduces a new spin field analogue for the relativistic RNS-particle in four dimensions, enabling a novel description of Ramond-Ramond states and their equations through cohomology, and explores related non-linear theories and sigma models.

Contribution

It presents a novel spin field construction for the RNS-particle, linking RR-fields to cohomology, and develops a sigma model framework to recover RNS formulation.

Findings

Cohomology matches RR-fields equations

Deformations encode background field effects

Sigma model reproduces RNS formulation

Abstract

We propose an analogue of spin fields for the relativistic RNS-particle in 4 dimensions, in order to describe Ramond-Ramond states as "two-particle" excitations on the world line. On a natural representation space we identify a differential whose cohomology agrees with RR-fields equations. We then discuss the non-linear theory encoded in deformations of the latter by background fields. We also formulate a sigma model for this spin field from which we recover the RNS-formulation by imposing suitable constraints.