Spectrum of conformal gauge theories on a torus

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 t. 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.