Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
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arXiv
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| Format: | Preprint |
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2024
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| author | Deddo, Evan Liu, James T. Zayas, Leopoldo A. Pando Saskowski, Robert J. |
| author_facet | Deddo, Evan Liu, James T. Zayas, Leopoldo A. Pando Saskowski, Robert J. |
| contents | 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 $\mathrm{AdS}_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows Deddo, Evan Liu, James T. Zayas, Leopoldo A. Pando Saskowski, Robert J. High Energy Physics - Theory 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 $\mathrm{AdS}_4$. |
| title | Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.15077 |