A note on gravity, entropy, and BF topological field theory

TL;DR

This paper derives the entropic force expression used in Verlinde's approach from first principles, assuming a topological BF theory coupled to particles as the microscopic foundation.

Contribution

It provides a novel derivation of entropic force from topological BF theory, connecting gravity, entropy, and topological field theory.

Findings

Entropic force expression can be derived from BF theory principles.

Topological BF theory offers a microscopic basis for Verlinde's gravity approach.

Links between topological field theories and emergent gravity are established.

Abstract

In this note I argue that the expression for entropic force, used as a starting point in Verlinde's derivation of Newton's law, can be deduced from first principles if one assumes that that the microscopic theory behind his construction is the topological $\SO(4,1)$ BF theory coupled to particles.