Spectrum of conformal gauge theories on a torus

TL;DR

This paper calculates the universal energy spectrum of QED3, a 2+1D conformal gauge theory with fermions, on a torus, revealing how topological degeneracies evolve with fermion inclusion in the large Nf limit.

Contribution

It provides the first explicit computation of the universal spectrum of QED3 on a torus, including effects of a Chern-Simons term, in the large Nf limit.

Findings

Universal spectrum of QED3 computed on a torus.

Demonstrated how topological degeneracy transforms with fermions.

Spectrum scales as 1/L times universal functions of the modular parameter τ.

Abstract

Many model quantum spin systems have been proposed to realize critical points or phases described by 2+1 dimensional conformal gauge theories. On a torus of size $L$ and modular parameter $\tau$, the energy levels of such gauge theories equal $(1/L)$ times universal functions of $\tau$. We compute the universal spectrum of QED$_3$, a U(1) gauge theory with $N_f$ two-component massless Dirac fermions, in the large $N_f$ limit. We also allow for a Chern-Simons term at level $k$, and show how the topological $k$-fold ground state degeneracy in the absence of fermions transforms into the universal spectrum in the presence of fermions; these computations are performed at fixed $N_f/k$ in the large $N_f$ limit.