Related papers: Higher holonomies: comparing two constructions

We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra.…

It is shown that the horizontal holonomy group of a K-contact sub-Riemannian manifold either coincides with the holonomy group of a Riemannian manifold, or it is a codimension-one normal subgroup of the later group. The question of…

Parallel transport, or path development, provides a rich characterization of paths which preserves the underlying algebraic structure of concatenation. The path signature is universal among such maps: any (translation-invariant) parallel…

We begin an investigation of inhomogeneous structures in holographic superfluids. As a first example, we study domain wall like defects in the 3+1 dimensional Einstein-Maxwell-Higgs theory, which was developed as a dual model for a…

The 2-blowup of a graph is obtained by replacing each vertex with two non-adjacent copies; a graph is biplanar if it is the union of two planar graphs. We disprove a conjecture of Gethner that 2-blowups of planar graphs are biplanar:…

A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…

In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional sigma models on special holonomy manifolds have extra symmetries that are in one-to-one correspondence with the covariantly constant forms on these manifolds. The…

This note is a contribution for a proceedings volume of the workshop "Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics". The content is a streamlined exposition based on a talk about a…

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge…

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on…

Surface holonomy and the Wess-Zumino phase play a central role in string theory and Chern-Simons models, yet a completely analytic formulation of their nonabelian counterparts has remained elusive. In this work, we show that Yekutieli's…

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a…

Arone and the second author showed that when the dimensions are in the stable range, the rational homology and homotopy of the high dimensional anologues of spaces of long knots can be calculated as the homology of a direct sum of finite…

We study (pre-)sheaves in bicategories on geometric categories: smooth manifolds, manifolds with a Lie group action and Lie groupoids. We present three main results: we describe equivariant descent, we generalize the plus construction to…

We show how the double vector bundle structure of the manifold of double velocities, with its submanifolds of holonomic and semiholonomic double velocities, is mirrored by a structure of holonomic and semiholonomic subgroups in the…

The notion of global higher-form symmetries has received much attention, but leaves room for a more systematic mathematical formulation. In this article, we highlight the concept of higher automorphism bundles from the field of higher…

Using finite abelian automorphism groups of $K3$ we construct orbifold candidates for Type IIA-heterotic dual pairs with maximal supersymmetry in six and lower dimensions. On the heterotic side, these results extend the series of known…

We describe a 2-dimensional analogue of track categories, called two-track categories, and show that it can be used to model categories enriched in 2-type mapping spaces. We also define a Baues-Wirsching type cohomology theory for track…

We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…

A theorem of Bergner, Osorno, Ozornova, Rovelli, and Scheimbauer states an equivalence between 2-Segal spaces and certain augmented stable double Segal spaces. In this paper we establish more general equivalences, involving simplicial maps…