Two-dimensional topological field theories coupled to four-dimensional BF theory

TL;DR

This paper develops new topological field theories coupling 2D world-sheet degrees of freedom, like Yang-Mills and tetrads, to 4D BF theory, aiming to explore background-independent quantum gravity models with emergent local degrees of freedom.

Contribution

It introduces coupled 2D topological theories with 4D BF theory, including Yang-Mills and tetrad fields, and discusses their quantization and relevance to quantum gravity.

Findings

Solutions correspond to Einstein equations with distributional matter.

Theories are argued to be exactly quantizable.

Potential for constructing background-independent quantum gravity models.

Abstract

Four dimensional BF theory admits a natural coupling to extended sources supported on two dimensional surfaces or string world-sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two dimensional world-sheet. We show how two dimensional Yang-Mills degrees of freedom can be added on the world-sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world-sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background independent quantum field theory where local degrees of freedom at low energies arise from global topological (world-sheet) degrees of freedom at the fundamental level.