Epsilon expansion for a Fermi gas at infinite scattering length

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We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over epsilon=4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/eF=1/2 epsilon³/2 + 1/16 epsilon⁵/2 ln epsilon -0.0246 epsilon⁵/2 and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu=2/epsilon-0.691. The minimum of the fermion dispersion curve is located at |p|=(2m epsilon₀)¹/2 where epsilon₀/mu=2+O(epsilon). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.