Advances in Theoretical and Mathematical Physics

Volume 11 (2007)

Number 3

Quantization of strings and branes coupled to BF theory

Pages: 451 – 469



John C. Baez

Alejandro Perez


BF theory is a topological theory that can be seen as a natural generalization of three-dimensional gravity to arbitrary dimensions. Here, we show that the coupling to point particles that is natural in three dimensions generalizes in a direct way to BF theory in $d$ dimensions coupled to $(d − 3)$-branes. In the resulting model, the connection is flat except along the membrane world-sheet, where it has a conical singularity whose strength is proportional to the membrane tension. As a step towards canonically quantizing these models, we show that a basis of kinematical states is given by "membrane spin networks", which are spin networks equipped with extra data where their edges end on a brane.

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