A Holographic c-Theorem for Schrodinger Spacetimes

TL;DR

This paper establishes a holographic c-theorem for Schrodinger spacetimes, showing the effective radius decreases monotonically along RG flows, independent of the critical exponent, with numerical examples illustrating the theory.

Contribution

It proves a c-theorem for Schrodinger holography that is valid for any critical exponent z and constructs explicit numerical solutions.

Findings

Effective radius L(r) decreases monotonically from UV to IR.

The c-theorem holds regardless of the value of z.

Numerical solutions with constant z=2 along the flow.

Abstract

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.