Towards the quantization of the non-relativistic D2-brane in the pure spinor formalism

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 Berkovits in (JHEP 04:018, arXiv:hep-th/0001035, 2000, JHEP 09:046, arXiv:hep-th/0006003, 2000, JHEP 09:016, arXiv:hep-th/0105050, 2001, ICTP Lect. Notes Ser. 13:57, arXiv:hep-th/0209059, 2003). 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.