Higher form Yang–Mills as higher BFYM theories

Abstract

The YM theory has been generalized to 2YM and 3YM theories. Similarly, we generalize the BFYM theory to “2BFYM” and “3BFYM” theories. Then, we show that these higher BFYM theories can give the formulations of the corresponding higher form YM theories. Finally, we study the gauge symmetries of these higher BFYM theories.

Higher Chern-Simons based on (2-)crossed modules

“…Then, we consider the differential forms valued in these associated algebras as follows. In this paper, we will mostly follow the notations and definitions of [24,59]. We denote by Λ k (M, g) the vector space of g-valued differential k-forms on a manifold M over C ∞ (M ).…”

“…For more properties for the Lie algebra valued differential forms corresponding to the identities of the differential (2-)crossed module, we refer the reader to [59].…”

“…See [31,37,38,58,61] for more details. The definitions and properties of the ordinary differential forms with values in differential crossed module and 2-crossed module have been introduced in our previous paper [59] and related work [24].…”

Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

“…In some of the modern approaches to the problem of quantum gravity based on the spinfoam formalism of loop quantum gravity [13,14], as well as in other applications of the so-called higher gauge theory (see [15] for a review and [16] for an application to quantum gravity), the description of gauge symmetry is being extended from the notion of a Lie group to different algebraic structures, called 2-groups, 3-groups, and in general, n-groups [17][18][19][20][21][22][23][24][25][26][27]. In this context, it is important to revisit and study the specific class of HT gauge symmetries, since they provide a nontrivial insight into the properties of these more general algebraic structures, as well as the physics behind the symmetries they describe.…”