A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories

TL;DR

This paper explores a series of stable, self-dual (2+1)d conformal field theories (CFTs) using duality, revealing their stability, boundary realizations, and phase transitions into fractional quantum Hall states, all through controlled calculations.

Contribution

It introduces a new duality framework to analyze stable (2+1)d self-dual CFTs without large flavor approximations, enhancing understanding of their boundary and phase transition properties.

Findings

CFTs can be realized on the boundary of (3+1)d topological insulators.

Dualities enable quantitative study of these CFTs.

Breaking time-reversal symmetry leads to fractional quantum Hall states.

Abstract

Using the duality between seemingly different (2+1)d conformal field theories (CFT) proposed recently, we study a series of (2+1)d stable self-dual interacting CFTs. These CFTs can be realized (for instance) on the boundary of the (3+1)d bosonic topological insulator protected by U(1) and time-reversal symmetry, and they remain stable as long as these symmetries are preserved. When realized as a boundary system, these CFTs can be driven into anomalous fractional quantum Hall states once time-reversal is broken. We demonstrate that the newly proposed dualities allow us to study these CFTs quantitatively through a controlled calculation, without relying on a large flavor number of matter fields.