Higher gauge theories based on 3-groups Radenković, T.; Vojinović, M.
The journal of high energy physics,
10/2019, Letnik:
2019, Številka:
10
Journal Article
Recenzirano
Odprti dostop
A
bstract
We study the categorical generalizations of a
BF
theory to 2
BF
and 3
BF
theories, corresponding to 2-groups and 3-groups, in the framework of higher gauge theory. In particular, we ...construct the constrained 3
BF
actions describing the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. The action is naturally split into a topological sector and a sector with simplicity constraints, adapted to the spinfoam quantization programme. In addition, the structure of the 3-group gives rise to a novel gauge group which specifies the spectrum of matter fields present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. This allows us to rewrite the whole Standard Model coupled to gravity as a constrained 3
BF
action, facilitating the nonperturbative quantization of both gravity and matter fields. Moreover, the presence and the properties of this new gauge group open up a possibility of a nontrivial unification of all fields and a possible explanation of fermion families and all other structure in the matter spectrum of the theory.
A
bstract
We study a generalization of 4-dimensional
BF
-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum
Z
, based on the classical 3
BF
...action for a general 3-group and a 4-dimensional spacetime manifold
M
4
. This state sum coincides with Porter’s TQFT for
d
= 4 and
n
= 3. In order to verify that the constructed state sum is a topological invariant of the underlying 4-dimensional manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum
Z
remains the same. This paper is a generalization of the work done by Girelli, Pfeiffer, and Popescu for the case of state sum based on the classical 2
BF
action with the underlying 2-group structure.
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