Probing holography in $p$-adic CFT

Abstract

We holographically calculate the partition functions of certain types of isotropic sectors of the CFTs dual to Bruhat-Tits trees and $p$-adic BTZ black holes. Along the way, we propose new spectral decompositions of the Laplacian operator other than the plane-wave basis on these two types of background, with both analytical and numerical evidence. We extract the density of states and hence entropy from the BTZ partition function via the inverse Laplace transform. Then the one-loop Witten diagram is computed in the $p$-adic BTZ black hole background, yielding constraints on the heavy-heavy-light averaged three-point coefficient of its boundary $p$-adic CFT. Finally, for general $p$-adic CFTs (not necessarily holographic), we analyze the representation theory of their global conformal group $PGL\left(2,{\mathbb{Q}}_p\right)$, and discuss the suitability of different representations as Hilbert spaces of $p$-adic CFT.

v3: 59 pages; published version

References in corpus (15)

• $T\bar{T}$ and the mirage of a bulk cutoff
• An exact quantization of Jackiw-Teitelboim gravity
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Sphere Packing and Quantum Gravity
• Fast Conformal Bootstrap and Constraints on 3d Gravity
• Harmonic analysis of 2d CFT partition functions
• 3D Gravity in a Box
• Geodesic bulk diagrams on the Bruhat-Tits tree
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Field Theory of Interacting Boundary Gravitons
• Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations
• Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree
• $T\overline{T}$-deformed free energy of the Airy model
• Effective field theory on a finite boundary of the Bruhat-Tits tree
• Adelic Amplitudes and Intricacies of Infinite Products

Cited by in corpus (2)

• Finite Temperature at Finite Places
• A glimpse into the Ultrametric spectrum