Adjusted parallel transport for higher gauge theories

Hyungrok Kim, Christian Saemann

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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.
Original languageEnglish
Article number445206
JournalJournal of Physics A: Mathematical and Theoretical
Volume53
Issue number44
Early online date14 Oct 2020
DOIs
Publication statusPublished - Nov 2020

Keywords

  • hep-th
  • math-ph
  • math.DG
  • math.MP

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