εexpansion of the conductivity at the superconductor-Mott-insulator transition

We study the critical behavior of the conductivity σ(ω) at the zero-temperature superconductor-Mott-insulator transition in d spacetime dimensions for a model of bosons with short-range interaction and no disorder. We obtain σ(ωₙ)=(4e²)σ_εωₙ^1-ε, as predicted by the scaling theory, and the prefactor σ_ε is calculated in the ε expansion, to order ε²(ε=4-d). In two spatial dimensions ($d=3$), we find a value of the universal conductance σ*=0.315(4e²h), in good agreement with the known Monte Carlo results.