Pure Spinors and D=6 Super-Yang-Mills

Abstract

Pure spinor cohomology has been used to describe maximally supersymmetric theories, like D=10 super-Yang-Mills and D=11 supergravity. Supersymmetry closes on-shell in such theories, and the fields in the cohomology automatically satisfy the equations of motion. In this paper, we investigate the corresponding structure in a model with off-shell supersymmetry, N=1 super-Yang-Mills theory in D=6. Here, fields and antifields are obtained as cohomologies in different complexes with respect to the BRST operator Q. It turns out to be natural to enlarge the pure spinor space with additional bosonic variables, subject to some constraints generalising the pure spinor condition, in order to accommodate the different supermultiplets in the same generalised pure spinor wave-function. We construct another BRST operator, s, acting in the cohomology of Q, whose cohomology implies the equations of motion. We comment on the possible use of similar approaches in other models.

11 pp, 3 figs, plain tex

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Cited by in corpus (7)

• Pure spinor superfields -- an overview
• N=8 superfield formulation of the Bagger-Lambert-Gustavsson model
• Superfield actions for N=8 and N=6 conformal theories in three dimensions
• Pure spinor superspace action for D=6, N=1 super-Yang-Mills theory
• The geometry of pure spinor space
• Superforms in Simple Six-dimensional Superspace
• Pure spinor superfields, with application to D=3 conformal models