Bubble Divergences from Cellular Cohomology View Full Text


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Article Info

DATE

2010-09

AUTHORS

Valentin Bonzom, Matteo Smerlak

ABSTRACT

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. More... »

PAGES

295-305

References to SciGraph publications

  • 2005-10. Group Field Theory: An Overview in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • 1993-01. Small volume limits of 2-d Yang-Mills in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1991-10. On quantum gauge theories in two dimensions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2000. An Introduction to Spin Foam Models of BF Theory and Quantum Gravity in GEOMETRY AND QUANTUM PHYSICS
  • 1989-09. Exactly soluble diffeomorphism invariant theories in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2011-05. Colored Group Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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