# Bounds on the local energy density of holographic CFTs from bulk geometry

@article{Fischetti2016BoundsOT, title={Bounds on the local energy density of holographic CFTs from bulk geometry}, author={Sebastian Fischetti and Andrew Hickling and Toby Wiseman}, journal={Classical and Quantum Gravity}, year={2016}, volume={33}, pages={225003} }

The stress tensor is a basic local operator in any field theory; in the context of AdS/CFT, it is the operator which is dual to the bulk geometry itself. Here we exploit this feature by using the bulk geometry to place constraints on the local energy density in static states of holographic (2+1)-dimensional CFTs living on a closed (but otherwise generally curved) spatial geometry. We allow for the presence of a marginal scalar deformation, dual to a massless scalar field in the bulk. For…

## 8 Citations

On universality of holographic results for (2 + 1)-dimensional CFTs on curved spacetimes

- Physics
- 2017

A bstractThe 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 space-time with compact…

A new energy bound for Einstein-Scalar theory in AlAdS$_4$ and holographic bound for deformed CFT$_3$

- Physics
- 2020

In this work, we derive an upper bound on energetic quantities, namely vacuum energy and free energy, for static solutions of Einstein-Scalar theory in four dimensional asymptotically locally Anti-de…

A bound on holographic entanglement entropy from inverse mean curvature flow

- Physics
- 2016

Entanglement entropies are notoriously difficult to compute. Large-N strongly-coupled holographic CFTs are an important exception, where the AdS/CFT dictionary gives the entanglement entropy of a CFT…

What Spatial Geometries do (2+1)-Dimensional Quantum Field Theory Vacua Prefer?

- PhysicsPhysical review letters
- 2018

It is shown that this quantum effect is non-negligible for the relativistic Dirac degrees of freedom on monolayer graphene even at room temperature, so it is argued that this vacuum energy effect should be included for a proper analysis of the equilibrium configuration of graphene or similar materials.

Conformally invariant averaged null energy condition from AdS/CFT

- PhysicsJournal of High Energy Physics
- 2020

We study the compatibility of the AdS/CFT duality with the bulk and boundary causality, and derive a conformally invariant averaged null energy condition (CANEC) for quantum field theories in 3 and…

A surprising similarity between holographic CFTs and a free fermion in (2 + 1) dimensions

- Physics
- 2021

We compare the behavior of the vacuum free energy (i.e. the Casimir energy) of various $(2+1)$-dimensional CFTs on an ultrastatic spacetime as a function of the spatial geometry. The CFTs we consider…

Does the round sphere maximize the free energy of (2+1)-dimensional QFTs?

- Physics
- 2020

We examine the renormalized free energy of the free Dirac fermion and the free scalar on a (2+1)-dimensional geometry $\mathbb{R} \times \Sigma$, with $\Sigma$ having spherical topology and…

The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality

- Physics
- 2020

We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the…

## References

SHOWING 1-10 OF 58 REFERENCES

AdS/CFT and the geometry of an energy gap

- Mathematics, Physics
- 2016

We consider a CFT defined on a static metric that is the product of time with a smooth closed space of positive scalar curvature. We expect the theory to exhibit an energy gap and our aim is to…

Vacuum energy is non-positive for (2 + 1)-dimensional holographic CFTs

- Physics
- 2016

We consider a (2 + 1)-dimensional holographic CFT on a static spacetime with globally timelike Killing vector. Taking the spatial geometry to be closed but otherwise general we expect a non-trivial…

Holographic thermal field theory on curved spacetimes

- Physics
- 2014

The AdS/CFT correspondence relates certain strongly-coupled CFTs with large effective central charge ceff to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in…

Some comments on gravitational entropy and the inverse mean curvature flow

- Mathematics
- 1999

The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem may be extended to give a negative lower bound for the mass of asymptotically anti-de Sitter spacetimes containing…

Quantum energy inequalities for the non-minimally coupled scalar field

- Physics, Mathematics
- 2007

In this paper, we discuss local averages of the energy density for the non-minimally coupled scalar quantum field, extending a previous investigation of the classical field. By an explicit example,…

Anti-de Sitter space and holography

- Physics
- 1998

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of…

The Large-N Limit of Superconformal Field Theories and Supergravity

- Physics, Mathematics
- 1997

We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes,…

A Stress Tensor for Anti-de Sitter Gravity

- Physics
- 1999

Abstract:We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered…

Lecture notes on holographic renormalization

- Physics
- 2002

We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of…