Flat space gravity at finite cutoff

TL;DR

This paper probes flat-space gravity at finite cutoff under conformal boundary conditions (CBC) and tests whether the boundary theory behaves as a local quantum field theory by matching bulk thermodynamics to a boundary thermal effective action. Using a saddle-point evaluation of the CBC bulk path integral, the authors extract Wilson coefficients $c_0$ and $c_1$ of the high-temperature expansion and find $c_0>0$ with a negative $c_1$, violating a QFT bound and suggesting gravity does not fully decouple at finite cutoff. The analysis is carried out for boundary geometries on $S^{d-1}$, $ ilde{eta}$-scaled flat horizons, and hyperbolic horizons, and is extended to non-spherical spaces where sign flips of odd-curvature contributions are observed in agreement with TEFT predictions. The results imply that the putative boundary dual is not a conventional QFT but is coupled to a dynamical metric, raising important questions about the interpretation of CBC in holography at finite cutoff and the role of curvature in boundary locality.

Abstract

We study the thermodynamics of Einstein gravity with vanishing cosmological constant subjected to conformal boundary conditions. Our focus is on comparing the series of subextensive terms to predictions from thermal effective field theory, with which we find agreement for the boundary theory on a spatial sphere, hyperbolic space, and flat space. We calculate the leading Wilson coefficients and observe that the first subextensive correction to the free energy is negative. This violates a conjectured bound on this coefficient in quantum field theory, which we interpret as a signal that gravity does not fully decouple in the putative boundary dual.

Figures (2)

• Figure 1: The Penrose diagram of the negative-mass hyperbolic black brane in AdS is presented on the left. A flat-space limit $\ell \rightarrow \infty$ gives the solution we use in this section, presented on the right with boundary cutoff $r_c$.
• Figure 2: The free energy diagram showing $GK^3F$ as a function of inverse conformal temperature $\tilde{\beta}$, as written in \ref{['freeenergy']}. The blue line is the Casimir energy, i.e. the free energy of the thermal gas. The red dashed line represents the small black hole, and the red solid line represents the large black hole. Both branches meet at the critical point $\tilde{\beta} = \pi$, but for $\tilde{\beta} < \pi$ the small black hole has the highest free energy and thus is subdominant in the ensemble. By contrast, the large black hole is dominant for temperatures above the Hawking--Page transition at $\tilde{\beta} = \sqrt{3}\pi/2$.