Spectrum of conformal gauge theories on a torus

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.

35 pages, additional figure in Appendix C

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Cited by in corpus (9)

• Gapless topological phases and symmetry-enriched quantum criticality
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Spectrum of the Wilson-Fisher conformal field theory on the torus
• Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point
• Quark distribution inside a pion in many-flavor (2 + 1)-dimensional QCD using lattice computations: UV listens to IR
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Monopole scaling dimension using Monte Carlo
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory