Extended matter coupled to BF theory

Winston J. Fairbairn and Alejandro Perez
Phys. Rev. D 78, 024013 – Published 8 July 2008

Abstract

Recently, a topological field theory of membrane matter coupled to BF theory in arbitrary spacetime dimensions was proposed [J. C. Baez and A. Perez, Adv. Theor. Math. Phys. 11, 3 (2007).]. In this paper, we discuss various aspects of the four-dimensional theory. First, we study classical solutions leading to an interpretation of the theory in terms of strings propagating on a flat spacetime. We also show that the general classical solutions of the theory are in one-to-one correspondence with solutions of Einstein’s equations in the presence of distributional matter (cosmic strings). Second, we quantize the theory and present, in particular, a prescription to regularize the physical inner product of the canonical theory. We show how the resulting transition amplitudes are dual to evaluations of Feynman diagrams coupled to three-dimensional quantum gravity. Finally, we remove the regulator by proving the topological invariance of the transition amplitudes.

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  • Received 28 January 2008

DOI:https://doi.org/10.1103/PhysRevD.78.024013

©2008 American Physical Society

Authors & Affiliations

Winston J. Fairbairn*

  • Laboratoire de Physique—CNRS-UMR 5672, ENS-Lyon, 46, Allée d’Italie, F-69364 Lyon, France, EU

Alejandro Perez

  • Centre de Physique Théorique‡—CNRS-UMR 6207, Luminy—Case 907, F-13288 Marseille, France, EU

  • *winston.fairbairn@ens-lyon.fr
  • perez@cpt.univ-mrs.fr
  • Unité mixte de recherche du CNRS et des Universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var. Laboratoire affilié à la FRUNAM (FR 2291).

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Issue

Vol. 78, Iss. 2 — 15 July 2008

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