de Sitter symmetry of Neveu-Schwarz spinors

TL;DR

This paper explores the relationship between Dirac fields on a 2D Lorentzian cylinder and de Sitter space, revealing extended de Sitter symmetry for Neveu-Schwarz anti-periodic fields and constructing the associated cocycle.

Contribution

It demonstrates the extended de Sitter covariance for Neveu-Schwarz Dirac fields and constructs the relevant cocycle, linking cylinder and de Sitter space symmetries.

Findings

Neveu-Schwarz anti-periodic Dirac fields exhibit extended de Sitter covariance

De Sitter symmetry is inherited by massless Neveu-Schwarz Dirac fields on the cylinder

Constructed the cocycle relating Dirac fields on different manifolds

Abstract

We study the relations between Dirac fields living on the 2-dimensional Lorentzian cylinder and the ones living on the double-covering of the 2-dimensional de Sitter manifold, here identified as a certain coset space of the group $SL(2,R)$. We show that there is an extended notion of de Sitter covariance only for Dirac fields having the Neveu-Schwarz anti-periodicity and construct the relevant cocycle. Finally, we show that the de Sitter symmetry is naturally inherited by the Neveu-Schwarz massless Dirac field on the cylinder.