Unitarity and universality in nonrelativistic conformal field theory

Abstract

We relate the notion of unitarity of a (0+1)-D conformally (SL(2,R)) invariant field theory with that of a nonrelativistic conformal (Schrödinger) field theory using the fact that SL(2,R) is a subgroup of nonrelativistic conformal (Schrödinger) group. Exploiting SL(2,R) unitarity, we derive the unitarity bounds and null conditions for a Schrödinger field theory (for the neutral as well as the charged sector). In noninteger dimensions the theory is shown to be nonunitary. The use of the SL(2,R) subgroup opens up the possibility of borrowing results from (0+1)-D SL(2,R) invariant field theory to explore Schrödinger field theory, in particular, the neutral sector, which has otherwise been unexplored.