Quantization of strings and branes coupled to BF theory

TL;DR

This paper extends BF theory to include coupling with (d-3)-branes in arbitrary dimensions, introduces membrane spin networks as a basis for quantization, and explores the resulting geometric and topological features.

Contribution

It generalizes the coupling of point particles in 3D BF theory to higher-dimensional branes and proposes membrane spin networks for canonical quantization.

Findings

Connection is flat except along brane world-sheets

Membrane spin networks form a basis of kinematical states

Conical singularities are proportional to membrane tension

Abstract

BF theory is a topological theory that can be seen as a natural generalization of 3-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.