A Holographic $c$-Theorem for Schrodinger Spacetimes

We prove a $c$-theorem for holographic renormalization group flows in a Schrodinger spacetime that demonstrates that the effective radius $L(r)$ monotonically decreases from the UV to the IR, where $r$ is the bulk radial coordinate. This result assumes that the bulk matter satisfies the null energy condition, but holds regardless of the value of the critical exponent $z$. We also construct several numerical examples in a model where the Schrodinger background is realized by a massive vector coupled to a real scalar. The full Schrodinger group is realized when $z=2$, and in this case it is possible to construct solutions with constant effective $z(r)=2$ along the entire flow.