Quantization of a Self-dual Conformal Theory in (2+1) Dimensions

TL;DR

This paper studies a (2+1)-dimensional nonlocal Abelian gauge theory, exploring its duality, spectrum, and conformal invariance, with implications for topological insulators and higher-dimensional theories.

Contribution

It provides a detailed quantization of a self-dual conformal theory in (2+1) dimensions, including spectrum calculations and duality properties, connecting to topological insulators.

Findings

Spectrum of electric and magnetic excitations computed

Theory exhibits conformal invariance on S^2 x S^1

Self-dual spectrum with fractional statistics identified

Abstract

Compact nonlocal Abelian gauge theory in (2+1) dimensions, also known as loop model, is a massless theory with a critical line that is explicitly covariant under duality transformations. It corresponds to the large N_F limit of self-dual electrodynamics in mixed three-four dimensions. It also provides a bosonic description for surface excitations of three-dimensional topological insulators. Upon mapping the model to a local gauge theory in (3+1) dimensions, we compute the spectrum of electric and magnetic solitonic excitations and the partition function on the three torus T_3. Analogous results for the S^2 x S^1 geometry show that the theory is conformal invariant and determine the manifestly self-dual spectrum of conformal fields, corresponding to order-disorder excitations with fractional statistics.