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Finite-cutoff holographic thermodynamics

Ming Zhang1,2,3,*, Wen-Di Tan4,†, Mengqi Lu1,‡, Dyuman Bhattacharya1,§, Jiayue Yang1,2,5,6,∥, and Robert B. Mann1,2,5,6,¶

  • *Contact author: mingchang@outlook.com
  • †Contact author: wendi.tan@ulb.be
  • ‡Contact author: m64lu@uwaterloo.ca
  • §Contact author: d7bhatta@uwaterloo.ca
  • ∥Contact author: j43yang@uwaterloo.ca
  • Contact author: rbmann@uwaterloo.ca
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Phys. Rev. Research 8, 013208 – Published 24 February, 2026

DOI: https://doi.org/10.1103/f94c-37sk

Abstract

We construct the first self-consistent framework for holographic thermodynamics in finite-cutoff holography, thereby capturing gravitational thermodynamics beyond the anti-de Sitter (AdS) boundary. We formulate two distinct first laws of thermodynamics: for the gravitational bulk, a Schwarzschild-AdS black hole with a finite Dirichlet cutoff, and for its dual T2 deformed conformal field theory (CFT) on the boundary. The central innovation is promoting the deformation parameter to a thermodynamic variable on the boundary, which maps precisely to the cutoff radius in the bulk. We demonstrate exact duality between these two thermodynamic laws, establishing a complete holographic dictionary. This framework reveals that the T2 deformation never lowers the confinement-deconfinement phase transition temperature below that of the original undeformed CFT, which acts as a global minimum. These results offer insights into gravitational thermodynamics with boundary constraints and quantum gravity in finite spacetime regions.

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Phys. Rev. Research 8, 013208– Published 24 February, 2026
  • Received 6 July 2025
  • Accepted 2 February 2026
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