  We review theoretical aspects of unitary Fermi gas (UFG), which has been
realized in ultracold atom experiments. We first introduce the epsilon
expansion technique based on a systematic expansion in terms of the
dimensionality of space. We apply this technique to compute the thermodynamic
quantities, the quasiparticle spectrum, and the critical temperature of UFG. We
then discuss consequences of the scale and conformal invariance of UFG. We
prove a correspondence between primary operators in nonrelativistic conformal
field theories and energy eigenstates in a harmonic potential. We use this
correspondence to compute energies of fermions at unitarity in a harmonic
potential. The scale and conformal invariance together with the general
coordinate invariance constrains the properties of UFG. We show the vanishing
bulk viscosities of UFG and derive the low-energy effective Lagrangian for the
superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic
scaling and conformal symmetries that can be in principle realized in ultracold
atom experiments.
