Abstract
We express supersymmetric couplings among the vector and the tensor multiplets in six dimensions (6D) in terms of N=1 superfields. The superfield description is derived from the invariant action in the projective superspace. The obtained expression is consistent with the known superfield actions of 6D supersymmetric gauge theory and 5D Chern-Simons theory after the dimensional reduction. Our result provides a crutial clue to the N=1 superfield description of 6D supergravity.
Highlights
The N = 1 superfield description of 5D SUGRA can be derived from the action in the projective superspace [8]
We have derived the N = 1 superfield description of supersymmetric coupling terms among 6D tensor and vector multiplets from the projective superspace action provided in ref
The tensor multiplet is described by two complex spinor superfields Yα and Zα, where Zα is constrained as D 2Zα = 0
Summary
An N = 2 off-shell action can be constructed by using the projective superspace formulation [16,17,18]. The 6D projective superspace is parametrized by the spacetime coodinates xM (M = 0, 1, · · · , 5), the Grassmannian coordinates Θiα (i = 1, 2; α = 1, 2, 3, 4), which form an SU(2)-Majorana-Weyl spinor, and the complex coordinate ζ of CP1. The constraint (2.3) fixes the dependence of Ξn on half of the Grassmann coordinates Θiα, and Ξn can be considered as superfields which effectively live on an N = 1 superspace. The natural conjugate operation in the projective superspace is the combination of the complex conjugate and the antipodal map on CP1 (ζ∗ → −1/ζ), which is called the smile conjugate denoted as (−1)nΞ−n(x, Θ)ζn. The action (2.5) is independent of η
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