Pure Spinor Formalism for Osp(N|4) backgrounds

TL;DR

This paper develops a pure spinor formalism for supercoset backgrounds based on Osp(N|4) superalgebras, deriving new constraints and constructing sigma models for AdS_4 x P^3, enabling consistent quantization.

Contribution

It introduces new pure spinor constraints from superalgebras and constructs quantizable sigma models for specific AdS backgrounds.

Findings

Derived new pure spinor constraints from superalgebras.

Constructed pure spinor and Green-Schwarz sigma models for AdS_4 x P^3.

Achieved consistent quantization of the pure spinor sigma model.

Abstract

We start from the Maurer-Cartan (MC) equations of the Osp(N|4) superalgebras satisfied by the left-invariant super-forms realized on supercoset manifolds of the corresponding supergroups and we derive some new pure spinor constraints. They are obtained by "ghostifying" the MC forms and extending the differential d to a BRST differential. From the superalgebras G =Osp(N|4) we single out different subalgebras H contained in G associated with the different cosets G/H: each choice of H leads to a different weakening of the pure spinor constraints. In each case, the number of parameter is counted and we show that in the cases of Osp(6|4)/U(3) x SO(1,3), Osp(4|4)/SO(3) x SO(1,3) and finally Osp(4|4) U(2)} x SO(1,3) the bosonic and fermionic degrees of freedom match in order to provide a c=0 superconformal field theory. We construct both the Green-Schwarz and the pure spinor sigma model for the case Osp(6|4)/U(3)x SO(1,3) corresponding to AdS_4 x P^3. The pure spinor sigma model can be consistently quantized.