Bubble divergences from cellular cohomology

Details Bubble divergences from cellular cohomology Bubble divergences from cellular cohomology

2010-04-29

arxiv.org/abs/1004.5196v2

Letters in Mathematical Physics 93, 3 (2010) 295-305

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages

Scientific paper

10.1007/s11005-010-0414-4

We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang-Mills theory, the Ponzano-Regge model of 3d quantum gravity and discrete BF theory, whose dynamical variables are flat discrete connections with compact structure group on a cell 2-complex. In these models, it is known that the path integral measure is ill-defined in general, because of a phenomenon called `bubble divergences'. A common expectation is that the degree of these divergences is given by the number of `bubbles' of the 2-complex. In this note, we show that this expectation, although not realistic in general, is met in some special cases: when the 2-complex is simply connected, or when the structure group is Abelian -- in both cases, the divergence degree is given by the second Betti number of the 2-complex.

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