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arXiv · 2404.15077

Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows

Evan Deddo·James T. Liu·Leopoldo A. Pando Zayas·Robert J. Saskowski
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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 $\mathrm{AdS}_{D+1}$ to $\mathrm{AdS}_3$ and prove the novel case of flows from $\mathrm{AdS}_5$ to $\mathrm{AdS}_4$.

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Evan Deddo, James T. Liu, Leopoldo A. Pando Zayas, Robert J. Saskowski. 2024-04-23. Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows. https://doi.org/10.1007/jhep09(2024)179

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