Bubble Divergences from Twisted Cohomology View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-06

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 and 3d Riemannian quantum gravity, 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 because of a phenomenon known as ‘bubble divergences’. In this paper, we extend recent results of the authors to the cases where these divergences cannot be understood in terms of cellular cohomology. We introduce in its place the relevant twisted cohomology, and use it to compute the divergence degree of the partition function. We also relate its dominant part to the Reidemeister torsion of the complex, thereby generalizing previous results of Barrett and Naish-Guzman. The main limitation to our approach is the presence of singularities in the representation variety of the fundamental group of the complex; we illustrate this issue in the well-known case of two-dimensional manifolds. More... »

PAGES

399-426

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
  • 2001. Introduction to Combinatorial Torsions in NONE
  • 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
  • 2010-09. Bubble Divergences from Cellular Cohomology in LETTERS IN MATHEMATICAL PHYSICS
  • 2011-05. Colored Group Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-012-1477-0

    DOI

    http://dx.doi.org/10.1007/s00220-012-1477-0

    DIMENSIONS

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