Quantization of strings and branes coupled to BF theory

Abstract

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.