Towards the quantization of the non-relativistic D2-brane in the Pure Spinor Formalism

TL;DR

This paper explores applying the pure spinor formalism to the non-relativistic IIA D2-brane, constructing a BRST charge and deriving constraints, including a novel solution involving pure spinors.

Contribution

It introduces a new approach to quantizing the non-relativistic D2-brane using pure spinor formalism and constructs a nilpotent BRST charge with a novel pure spinor solution.

Findings

Constructed fermionic constraints for the non-relativistic D2-brane.

Developed a BRST charge using Berkovits' ansatz.

Found a new pure spinor solution as a sum of two pure spinors.

Abstract

An attempt is made to apply the pure spinor formalism to the non-relativistic IIA D2-brane. The fermionic constraints corresponding to the rescaled fermionic coordinates are given. Two commuting spinor fields are introduced, each one corresponding to a fermionic constraint. A BRST charge is constructed via the ansatz proposed by N. Berkovits. The nilpotency of the BRST charge leads to a set of constraints for the two spinor fields including pure spinor constraints. A novel non-trivial solution is given for one of the spinor fields which can be written as a sum of two pure spinors.