2022/05/26 by Florian Girelli, Girelli, Florian, Matteo Laudonio +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2205.13312
We introduce the framework of Hopf algebra field theory (HAFT) which\ngeneralizes the notion of group field theory to the quantum group (Hopf\nalgebra) case. We focus in particular on the 3d case and show how the HAFT we\nconsidered is topological. The highlight of the construction is the notion of\nplane-wave which leads, in the specific example of SUq (2) with q real, to a\ndiscretization of the Euclidian BF action with a negative cosmological\nconstant. This work can be viewed as the generalization of the seminal work by\nBaratin and Oriti: we have a (non-commutative) formulation of simplicial 3d\ngravity in the presence of a non-zero cosmological constant.\n