scholarly journals A global perspective to connections on principal 2-bundles

2018 ◽  
Vol 30 (4) ◽  
pp. 809-843 ◽  
Author(s):  
Konrad Waldorf
Keyword(s):  
Gauge Theory ◽  
Differential Forms ◽  
Adjoint Action ◽  
Global Perspective ◽  
Lie Groupoids ◽  
Classification Result ◽  
Differential Cohomology ◽  
Lie Groupoid ◽  
Higher Gauge Theory ◽  
Complete Analogy

Abstract For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define connections on principal 2-bundles as Lie 2-algebra-valued 1-forms on the total space Lie groupoid of the 2-bundle, satisfying a condition in complete analogy to connections on ordinary principal bundles. We carefully treat various notions of curvature, and prove a classification result by the non-abelian differential cohomology of Breen–Messing. This provides a consistent, global perspective to higher gauge theory.

scholarly journals Six-dimensional (1,0) superconformal models and higher gauge theory

2013 ◽  
Vol 54 (11) ◽  
pp. 113509 ◽  
Author(s):  
Sam Palmer ◽  
Christian Sämann
Keyword(s):  
Gauge Theory ◽  
Higher Gauge Theory

scholarly journals On local integration of Lie brackets

2020 ◽  
Vol 2020 (760) ◽  
pp. 267-293 ◽  
Author(s):  
Alejandro Cabrera ◽  
Ioan Mărcuţ ◽  
María Amelia Salazar
Keyword(s):  
Vector Field ◽  
Lie Algebroids ◽  
Lie Algebroid ◽  
Lie Theory ◽  
Lie Groupoids ◽  
Lie Groupoid ◽  
Finite Dimensional ◽  
Local Integration ◽  
Lie Brackets ◽  
Complete Account

AbstractWe give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field lifting the underlying anchor map. This construction leads to a complete account of local Lie theory and, in particular, to a finite-dimensional proof of the fact that the category of germs of local Lie groupoids is equivalent to that of Lie algebroids.

scholarly journals HIGHER GAUGE THEORY AND GRAVITY IN 2+1 DIMENSIONS

2007 ◽  
Vol 22 (28) ◽  
pp. 5155-5172 ◽  
Author(s):  
R. B. MANN ◽  
E. M. POPESCU
Keyword(s):  
Gauge Theory ◽  
Two Dimensional ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Present Context ◽  
Dimensional Gravity ◽  
Wide Perspective ◽  
Higher Gauge Theory ◽  
Matter Fields ◽  
New Framework

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson–Friedman–Walker cosmological-like expanding geometries — this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in 2+1 dimensions coupled to matter in an entirely new framework.

scholarly journals Deformations of Lie Groupoids

2018 ◽  
Vol 2020 (21) ◽  
pp. 7662-7746 ◽  
Author(s):  
Marius Crainic ◽  
João Nuno Mestre ◽  
Ivan Struchiner
Keyword(s):  
Normal Form ◽  
Adjoint Representation ◽  
Lie Groupoids ◽  
Lie Groupoid ◽  
Fundamental Properties

Abstract We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance, a van Est theorem, and a vanishing result in the proper case. Combined with Moser’s deformation arguments for groupoids, we obtain several rigidity and normal form results.

scholarly journals The ABJM model is a higher gauge theory

2014 ◽  
Vol 11 (08) ◽  
pp. 1450075 ◽  
Author(s):  
Sam Palmer ◽  
Christian Sämann
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Higher Gauge Theory ◽  
Brane Models

M2-branes couple to a 3-form potential, which suggests that their description involves a non-abelian 2-gerbe or, equivalently, a principal 3-bundle. We show that current M2-brane models fit this expectation: they can be reformulated as higher gauge theories on such categorified bundles. We thus add to the still very sparse list of physically interesting higher gauge theories.

scholarly journals Riemannian metrics on Lie groupoids

2018 ◽  
Vol 2018 (735) ◽  
pp. 143-173 ◽  
Author(s):  
Matias del Hoyo ◽  
Rui Loja Fernandes
Keyword(s):  
Riemannian Metrics ◽  
Exponential Map ◽  
Important Class ◽  
Lie Groupoids ◽  
Lie Groupoid ◽  
Linearization Theorem

AbstractWe introduce a notion of metric on a Lie groupoid, compatible with multiplication, and we study its properties. We show that many families of Lie groupoids admit such metrics, including the important class of proper Lie groupoids. The exponential map of these metrics allows us to establish a linearization theorem for Riemannian groupoids, obtaining both a simpler proof and a stronger version of the Weinstein–Zung linearization theorem for proper Lie groupoids. This new notion of metric has a simplicial nature which will be explored in future papers of this series.

scholarly journals Higher gauge theory—differential versus integral formulation

2004 ◽  
Vol 45 (10) ◽  
pp. 3949-3971 ◽  
Author(s):  
Florian Girelli ◽  
Hendryk Pfeiffer
Keyword(s):  
Gauge Theory ◽  
Integral Formulation ◽  
Higher Gauge Theory
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