Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space

Abstract

We construct manifestly superconformal field theories in six dimensions which contain a non-Abelian tensor multiplet. In particular, we show how principal 3-bundles over a suitable twistor space encode solutions to these self-dual tensor field theories via a Penrose-Ward transform. The resulting higher or categorified gauge theories significantly generalise those obtained previously from principal 2-bundles in that the so-called Peiffer identity is relaxed in a systematic fashion. This transform also exposes various unexplored structures of higher gauge theories modelled on principal 3-bundles such as the relevant gauge transformations. We thus arrive at the non-Abelian differential cohomology that describes principal 3-bundles with connective structure. © 2014 Springer Science+Business Media Dordrecht

The (2, 0) superconformal bootstrap

“…It is unclear whether an unconventional (nonlocal?) Lagrangian for the interacting (2, 0) theories could be written down (see, e.g., [21][22][23][24][25][26] for a partial list of attempts), but in any event it would be unlikely to lend itself to a semiclassical approximation.…”

“…26 Suppose that the approximate solution to crossing symmetry obtained at c min with finite Λ has a small bias: instead of a B½0; 2 1 block it has an L½0; 0 Δ 2 ;2 block which sits just above the unitarity bound. As in the scalar and spin four channel, the presence of such a block would technically imply step function behavior of the bound at c min , but since the block appears only slightly above the unitarity bound the step can be quite small and we would not observe it in Fig.…”

Superforms in six-dimensional superspace

“…28 Work is currently underway to investigate this idea and extend it to the full non-abelian hierarchy. For recent closely-related work on such a construction for the bosonic part of the non-abelian tensor hierarchy, see [80,81] and references therein.…”

“…In section 6.2 we connect this construction to the sourced and composite p-form complices of sections 4 and 5. For recent work in this direction, see [80,81].…”

Higher Structures, Self‐Dual Strings and 6d Superconformal Field Theories

“…[27] Vanishing of the fake curvature also arises naturally in twistor descriptions based on conventional higher holomorphic principal bundles. [26,[28][29][30] One could now consider the condition F = 0 as an equation of motion and postulate that the above relation (13) indicates an "open symmetry," which closes only up to equations of motion. This interpretation, however, leads to another problem.…”