Extended matter coupled to BF theory

Winston J. Fairbairn (1) , Alejandro Perez (2, 3)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, 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). Secondly, 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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Winston J. Fairbairn, Alejandro Perez. Extended matter coupled to BF theory. Physical Review D, 2008, 78 (2). ⟨hal-00175142⟩