Semistrict higher gauge theory

Abstract

We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from theČech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due toŠevera. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a nonAbelian N = (2, 0) tensor multiplet taking values in a semistrict Lie 2-algebra.

Higher Geometry for Non-geometric T-Duals

“…The Γ-cocycles for semi-strict Lie 2-groups have been worked out in [JSW15]. With respect to an open cover {U i } i∈I , they are pairs (g, γ) consisting of smooth maps g ij : U i ∩ U j → Ob(Γ) and γ ijk : U i ∩ U j ∩ U k → Mor(Γ) such that the following conditions are satisfied:…”

A new formulation of higher parallel transport in higher gauge theory

“…Our interest in this subject has been prompted by our recent formulation of semistrict higher gauge theory aimed to higher Chern-Simons theory, in which we circumvent the difficulties related to the integration of the underlying semistrict Lie 2-algebra to a semistrict 2-group, when possible, by relying on the automorphism 2-group of the Lie 2-algebra, which is always strict [27,28]. (See also [29] for an alternative approach.) In a companion paper, we plan to study the issue of higher holonomy and invariant traces on the same lines [30].…”

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

“…Finally, let us stress that most of the problems we encountered with our action can be circumvented when discussing merely equations of motion. In our previous work [26,[28][29][30] we found a description of solutions to these equations in terms of holomorphic categorified principal bundles over a suitable twistor space. This essentially reduced the search for classical equations of the (2,0)theory to a search for the right gauge structure (which implies a notion of holomorphic categorified principal bundle).…”

“…Here we shall take a slight shortcut as done e.g. in [26]. We note that L ∞ -algebras are generalizations of differential graded Lie algebras.…”

“…[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.…”