Conformal Boundary Conditions from Cutoff AdS${}_3$

Abstract

We construct a particular flow in the space of 2D Euclidean QFTs on a torus, which we argue is dual to a class of solutions in 3D Euclidean gravity with conformal boundary conditions. This new flow comes from a Legendre transform of the kernel which implements the $T\bar{T}$ deformation, and is motivated by the need for boundary conditions in Euclidean gravity to be elliptic, i.e. that they have well-defined propagators for metric fluctuations. We demonstrate equivalence between our flow equation and variants of the Wheeler de-Witt equation for a torus universe in the so-called Constant Mean Curvature (CMC) slicing. We derive a kernel for the flow, and we compute the corresponding ground state energy in the low-temperature limit. Once deformation parameters are fixed, the existence of the ground state is independent of the initial data, provided the seed theory is a CFT. The high-temperature density of states has Cardy-like behavior, rather than the Hagedorn growth characteristic of $T\bar{T}$-deformed theories.

arXiv comment17 pages, 0 figures

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• Q-curvature and Path Integral Complexity
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• Supersymmetric black holes and $T\bar{T}$ deformation
• Holographic entanglement entropy and mutual information in deformed field theories at finite temperature
• Mixed state entanglement in deformed field theory at finite temperature
• A substrate for brane shells from $T\bar{T}$
• York time in JT gravity