Abstract
A Batalin-Vilkovisky action for D = 6, N = 1 super-Yang-Mills theory, including coupling to hypermultiplets, is given. The formalism involves pure spinor superfields. The geometric properties of the D = 6, N = 1 pure spinors (which differ from Cartan pure spinors) are examined. Unlike the situation for maximally supersymmetric models, the fields and antifields (including ghosts) of the vector multiplet reside in separate superfields. The formalism provides an off-shell superspace formulation for matter hypermultiplets, which in a traditional treatment are on-shell.
Highlights
2.1 Minimal pure spinor variables The important property for pure spinors in relation to supersymmetry is the constraint = 0
The multiplet is an on-shell multiplet in the traditional sense, and QΦ = 0 implies the component equations of motion. This is in complete agreement with a traditional superspace formulation of the hypermultiplet, where the scalar multiplet consists of the ghost number 0 part of Φ
We have presented a classical Batalin-Vilkovisky action for chiral D = 6 SYM theory
Summary
If superfields are functions of the non-minimal variables xa, θα, λα, λα and dλα, they are forms with antiholomorphic indices on complex pure spinor space. From the description of pure spinor space as C4 × CP 1, it is clear that there is one, but three holomorphic 5-forms, which can be written as d4y zpdz, p = 0, 1, 2, where y parametrises C4 and z CP 1 They transform as a triplet under R-symmetry. The radial integral behaves as d 9+2p, and converges at = 0 if p > −5 This is minus the complex dimension of pure spinor space, which is a generic feature. If e.g. gauge variations of the fields, in the form of BRST variations or shift symmetries (to be discussed later) are considered, they must obey the corresponding regularity condition
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