Pure Spinor Formalism for Osp(N|4) backgrounds

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.

25 pp, latex, Misprints, improvements in the last section and references added

References in corpus (17)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Comments on the Bagger-Lambert theory and multiple M2-branes
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• On Type IIA Penrose Limit and N=6 Chern-Simons Theories
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Finite size Giant Magnons in the string dual of N=6 superconformal Chern-Simons theory
• Towards a Worldsheet Derivation of the Maldacena Conjecture
• Superstrings on AdS_4 x CP^3 from Supergravity
• A New Limit of the AdS_5 x S^5 Sigma Model
• Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds
• Free Differential Algebras, Rheonomy, and Pure Spinors
• Pure Spinors for General Backgrounds

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• The higher-algebraic skeleton of the superstring -- a case study
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