Gravitational Dressing of Aharonov-Bohm Amplitudes

TL;DR

This paper explores how gravitational effects modify Aharonov-Bohm scattering amplitudes in a topologically massive gauge and gravity theory, revealing deep connections with conformal field theory and implications for string theory reformulations.

Contribution

It demonstrates a novel relationship between gravitationally dressed spins in a topologically massive theory and conformal weights, extending known Chern-Simons gauge theory results.

Findings

Transmuted spins relate to Chern-Simons theory via a KZ-like formula.

Gravitational dressing affects Aharonov-Bohm amplitudes.

Implications for topological membrane and string reformulations.

Abstract

We investigate Aharonov-Bohm scattering in a theory in which charged bosonic matter fields are coupled to topologically massive electrodynamics and topologically massive gravity. We demonstrate that, at one-loop order, the transmuted spins in this theory are related to the ones of ordinary Chern-Simons gauge theory in the same way that the Knizhnik-Polyakov-Zamolodchikov formula relates the Liouville-dressed conformal weights of primary operators to the bare weights in two-dimensional conformal field theories. We remark on the implications of this connection between two-dimensional conformal field theories and three-dimensional gauge and gravity theories for a topological membrane reformulation of strings. We also discuss some features of the gravitational analog of the Aharonov-Bohm effect.