Non-Abelian Tensor Multiplet Equations from Twistor Space

Abstract

We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N = (1,0) and N = (2,0) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings. © 2014 Springer-Verlag Berlin Heidelberg

Chern-Simons actions and their gaugings in 4D, N =1 superspace

“…[13], and take its variations, we need to make a couple of definitions, 6) and another application of the Chern-Simons superfield construction, where we are given three arguments, one of which is a chiral spinor superfield ψ and the other two are real scalar superfields U 1 and U 2 . Then we have…”

“…[4] all vector fields (abelian and non-abelian) are treated on the same footing and the tensor analogous to the map (2.11) is naturally symmetric 6 in contrast to the asymmetric cases considered here. 6 More explicitly, once we combine g and V1 into a single vector space V1 = V1 ⊕ g, then the analog of (2.11) for r = 1 is…”

“…[13], which was invariant in the abelian case and correctly reproduced the bosonic Chern-Simons action (5. +α 6 (Σ α , E, W α ) + α 9 (Γ, E, E)) . (6.10)…”

“…Consistency of the resulting "non-abelian tensor hierarchy" requires a complicated set of identities to hold between the Lie algebra, its representations, and a collection of maps relating the forms of various degrees [4,5]. Attempts at interpreting this structure algebro-geometrically suggest that they are strongly homotopy Lie algebras [6,7].…”

Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets

“…In [4] this problem was encompassed in the context of a tensor hierarchy [5,6] by introducing additional form-degrees of freedom, in particular an ordinary gauge field and non-propagating three-and (optionally) four-form gauge fields. This structure shows similarity with concepts of higher gauge theories, Q structures, and non-abelian gerbes [7][8][9][10][11][12], extended to higher degree forms. A very particular realization of this gauge symmetry was given in [13].…”