Nonrelativistic CFTs at large charge: Casimir energy and logarithmic enhancements

Abstract

The unitary Fermi gas, by virtue of its description as a nonrelativistic conformal field theory, has proven an interesting system by which the quantum properties of CFTs can be held to experimental verification. Here, we examine the structure of conformal dimensions of charge-Q operators in nonrelativistic CFTs, in the large-Q regime, from the non-linear sigma model perspective. We discuss in detail the renormalization of edge divergences using dimensional regularization, elucidating the presence of log(Q) terms in the large-charge expansion. Finally, we use dimensional regularization to compute the universal one-loop Q0 log Q contribution to the ground-state energy in d = 3 spatial dimensions, with the result Delta {(Q)}_{Q^0}=frac{1}{3sqrt{3}}log (Q)+ const.