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Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows by Deddo, Evan; Liu, James T.; Zayas, Leopoldo A. Pando; Saskowski, Robert J. is a scholarly article available to read on EtoBox.

What is Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows about?

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 $\mathrm{AdS}_{D+1}$ to $\mathrm{AdS}_3$ and prove the novel case of flows from $\mathrm{AdS}_5$ to $\mathrm{AdS}_4$.

Author

Deddo, Evan; Liu, James T.; Zayas, Leopoldo A. Pando; Saskowski, Robert J.

Published

2024

Language

EN