The paper constructs ribbon balancing data and framing levels for 2Rep(U_q G), making it a candidate ribbon tensor 2-category, and recovers strict pivotality in the classical limit q=1.
Poincare 2-group and quantum gravity
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abstract
We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge lengths of the spacetime manifold triangulation arise as the basic variables in the path-integral quantization, while the state-sum amplitude is an evaluation of a colored 3-complex, in agreement with the category theory results. A 3-complex amplitude for Euclidean quantum gravity is proposed.
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Categorical quantum symmetries and ribbon tensor 2-categories
The paper constructs ribbon balancing data and framing levels for 2Rep(U_q G), making it a candidate ribbon tensor 2-category, and recovers strict pivotality in the classical limit q=1.