On Universality of Holographic Results for (2+1)-Dimensional CFTs on Curved Spacetimes

TL;DR

This paper demonstrates that certain energy and spectral bounds in (2+1)-dimensional CFTs, previously thought to be holographic-specific, are actually universal across all CFTs due to fundamental correlator behaviors.

Contribution

It establishes the universality of energy and spectral bounds in (2+1)-D CFTs, extending results beyond holographic theories through correlator analysis.

Findings

Vacuum energy is nonpositive for all CFTs on static spacetimes.

Energy density bounds hold universally for perturbations around backgrounds.

Negativity properties of vacuum energy extend globally across spatial geometries.

Abstract

The behavior of holographic CFTs is constrained by the existence of a bulk dual geometry. For example, in (2+1)-dimensional holographic CFTs living on a static spacetime with compact spatial slices, the vacuum energy must be nonpositive, certain averaged energy densities must be nonpositive, and the spectrum of scalar operators is bounded from below by the Ricci scalar of the CFT geometry. Are these results special to holographic CFTs? Here we show that for perturbations about appropriate backgrounds, they are in fact universal to all CFTs, as they follow from the universal behavior of two- and three-point correlators of known operators. In the case of vacuum energy, we extend away from the perturbative regime and make global statements about its negativity properties on the space of spatial geometries. Finally, we comment on the implications for dynamics which are dissipative and driven by such a vacuum energy and we remark on similar results for the behavior of the Euclidean partition function on deformations of flat space or the round sphere.