Explicit entropic proofs of irreversibility theorems for holographic RG flows
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2024)179 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |