Explicit entropic proofs of irreversibility theorems for holographic RG flows - Evan Deddo; James T. Liu; Leopoldo A. Pando Zayas; Robert J. Saskowski (Journal of High Energy Physics, 2024)
Abstract We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the c-, F -, and a-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a holographic c-function that is monotonic along the flow. We then apply our method to the case of flows across dimensions: there, we reprove the monotonicity of flows from AdS D+1 to AdS3 and prove the novel case of flows from AdS5 to AdS4.