Adjusted Parallel Transport for Higher Gauge Theories

Abstract

Many physical theories, including notably string theory, require non-abelian higher gauge fields defining higher holonomy. Previous approaches to such higher connections on categorified principal bundles require these to be fake flat. This condition, however, renders them locally gauge equivalent to connections on abelian gerbes. For particular higher gauge groups, for example 2-group models of the string group, this limitation can be overcome by generalizing the notion of higher connection. Starting from this observation, we define a corresponding generalized higher holonomy functor which is free from the fake flatness condition, leading to a truly non-abelian parallel transport.

arXiv commentv2: 56 pages, presentation improved, minor error corrected, published version

References in corpus (33)

• Closed String Field Theory: Quantum Action and the BV Master Equation
• Introduction to string field theory
• Introduction to sh Lie algebras for physicists
• Higher-Dimensional Algebra V: 2-Groups
• An Invitation to Higher Gauge Theory
• A New Approach to Integrable Theories in any Dimension
• Twisted differential String and Fivebrane structures
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Higher Gauge Theory: 2-Connections on 2-Bundles
• Geometry of Deligne cohomology
• Higher Yang-Mills Theory
• Parallel Transport and Functors
• Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory
• Central Extensions of Smooth 2-Groups and a Finite-Dimensional String 2-Group
• Higher gauge theory -- differential versus integral formulation
• Butterflies I: morphisms of 2-group stacks
• L-infinity algebra connections and applications to String- and Chern-Simons n-transport
• The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module
• Towards an M5-Brane Model I: A 6d Superconformal Field Theory
• Semistrict Higher Gauge Theory
• A new formulation of higher parallel transport in higher gauge theory
• Non-Abelian Wilson Surfaces
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps
• The inner automorphism 3-group of a strict 2-group
• Towards an M5-Brane Model II: Metric String Structures
• The Non-Abelian Self-Dual String and the (2,0)-Theory
• Canonical gauges in higher gauge theory
• Generalized Higher Gauge Theory
• Higher Gauge Theory with String 2-Groups
• On the global $2$-holonomy for a $2$-connection on a $2$-bundle
• Twisted Weil Algebras for the String Lie 2-Algebra
• A Global Geometric Approach to Parallel Transport of Strings in Gauge Theory

Cited by in corpus (12)

• Orbifolds by 2-groups and decomposition
• Towards an M5-Brane Model III: Self-Duality from Additional Trivial Fields
• (2-)Drinfel'd Double and (2-)BF Theory
• Higher Gauge Theory and Integrability
• Higher Gauge Theory
• Surface Operators in Superspace
• 2-Drinfel'd double symmetry of the 4d Kitaev model
• Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
• Explicit Non-Abelian Gerbes with Connections
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies
• Adjusting Higher Chern-Simons Theory
• Extended Field Theories as higher Kaluza-Klein theories