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

Herrera-Aguilar, A.  (Aff1, 0000 0001 2112 2750, grid.411659.e, Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, Puebla, Mexico) (Aff2, 0000 0000 8796 243X, grid.412205.0, Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, CP 58040, Morelia, Michoacán, Mexico) ; Paschalis, J. E. (Aff3, 0000000109457005, grid.4793.9, Theoretical Physics Department, Aristotle University of Thessaloniki, 54124, Thessaloníki, Greece)

18 June 2019

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.

Published in: EPJC 79 (2019) 521 DOI: 10.1140/epjc/s10052-019-6999-6