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Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
- Source :
- JHEP 09 (2024) 179
- Publication Year :
- 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 $\mathrm{AdS}_{D+1}$ to $\mathrm{AdS}_3$ and prove the novel case of flows from $\mathrm{AdS}_5$ to $\mathrm{AdS}_4$.<br />Comment: 28 pages, 3 figures; references added
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- JHEP 09 (2024) 179
- Publication Type :
- Report
- Accession number :
- edsarx.2404.15077
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP09(2024)179