91 research outputs found
Bulk Connectedness and Boundary Entanglement
We prove, for any state in a conformal field theory defined on a set of
boundary manifolds with corresponding classical holographic bulk geometry, that
for any bipartition of the boundary into two non-clopen sets, the density
matrix cannot be a tensor product of the reduced density matrices on each
region of the bipartition. In particular, there must be entanglement across the
bipartition surface. We extend this no-go theorem to general, arbitrary
partitions of the boundary manifolds into non-clopen parts, proving that the
density matrix cannot be a tensor product. This result gives a necessary
condition for states to potentially correspond to holographic duals.Comment: 12 pages, 2 figure
Hidden Simplicity of the Gravity Action
We derive new representations of the Einstein-Hilbert action in which
graviton perturbation theory is immensely simplified. To accomplish this, we
recast the Einstein-Hilbert action as a theory of purely cubic interactions
among gravitons and a single auxiliary field. The corresponding equations of
motion are the Einstein field equations rewritten as two coupled first-order
differential equations. Since all Feynman diagrams are cubic, we are able to
derive new off-shell recursion relations for tree-level graviton scattering
amplitudes. With a judicious choice of gauge fixing, we then construct an
especially compact form for the Einstein-Hilbert action in which all graviton
interactions are simply proportional to the graviton kinetic term. Our results
apply to graviton perturbations about an arbitrary curved background spacetime.Comment: 20 pages, 1 figur
Infrared Consistency and the Weak Gravity Conjecture
The weak gravity conjecture (WGC) asserts that an Abelian gauge theory
coupled to gravity is inconsistent unless it contains a particle of charge
and mass such that . This criterion is obeyed by all
known ultraviolet completions and is needed to evade pathologies from stable
black hole remnants. In this paper, we explore the WGC from the perspective of
low-energy effective field theory. Below the charged particle threshold, the
effective action describes a photon and graviton interacting via
higher-dimension operators. We derive infrared consistency conditions on the
parameters of the effective action using i) analyticity of light-by-light
scattering, ii) unitarity of the dynamics of an arbitrary ultraviolet
completion, and iii) absence of superluminality and causality violation in
certain non-trivial backgrounds. For convenience, we begin our analysis in
three spacetime dimensions, where gravity is non-dynamical but has a physical
effect on photon-photon interactions. We then consider four dimensions, where
propagating gravity substantially complicates all of our arguments, but bounds
can still be derived. Operators in the effective action arise from two types of
diagrams: those that involve electromagnetic interactions (parameterized by a
charge-to-mass ratio ) and those that do not (parameterized by a
coefficient ). Infrared consistency implies that is bounded from
below for small .Comment: 37 pages, 5 figures. Minor typos fixed and equation numbers changed
to match journal. Published in JHE
Quantum Gravity Constraints from Unitarity and Analyticity
We derive rigorous bounds on corrections to Einstein gravity using unitarity
and analyticity of graviton scattering amplitudes. In spacetime
dimensions, these consistency conditions mandate positive coefficients for
certain quartic curvature operators. We systematically enumerate all such
positivity bounds in and before extending to . Afterwards,
we derive positivity bounds for supersymmetric operators and verify that all of
our constraints are satisfied by weakly-coupled string theories. Among
quadratic curvature operators, we find that the Gauss-Bonnet term in
is inconsistent unless new degrees of freedom enter at the natural cutoff scale
defined by the effective theory. Our bounds apply to perturbative ultraviolet
completions of gravity.Comment: 26 page
Proof of the Weak Gravity Conjecture from Black Hole Entropy
We prove that higher-dimension operators contribute positively to the entropy
of a thermodynamically stable black hole at fixed mass and charge. Our results
apply whenever the dominant corrections originate at tree level from quantum
field theoretic dynamics. More generally, positivity of the entropy shift is
equivalent to a certain inequality relating the free energies of black holes.
These entropy inequalities mandate new positivity bounds on the coefficients of
higher-dimension operators. One of these conditions implies that the
charge-to-mass ratio of an extremal black hole asymptotes to unity from above
for increasing mass. Consequently, large extremal black holes are unstable to
decay to smaller extremal black holes and the weak gravity conjecture is
automatically satisfied. Our findings generalize to arbitrary spacetime
dimension and to the case of multiple gauge fields. The assumptions of this
proof are valid across a range of scenarios, including string theory
constructions with a dilaton stabilized below the string scale.Comment: 35 pages, 2 figure
Splitting Spacetime and Cloning Qubits: Linking No-Go Theorems across the ER=EPR Duality
We analyze the no-cloning theorem in quantum mechanics through the lens of
the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between
entanglement and wormholes. In particular, we find that the no-cloning theorem
is dual on the gravity side to the no-go theorem for topology change, violating
the axioms of which allows for wormhole stabilization and causality violation.
Such a duality between important no-go theorems elucidates the proposed
connection between spacetime geometry and quantum entanglement.Comment: 6 pages, 2 figure
Entanglement Conservation, ER=EPR, and a New Classical Area Theorem for Wormholes
We consider the question of entanglement conservation in the context of the
ER=EPR correspondence equating quantum entanglement with wormholes. In quantum
mechanics, the entanglement between a system and its complement is conserved
under unitary operations that act independently on each; ER=EPR suggests that
an analogous statement should hold for wormholes. We accordingly prove a new
area theorem in general relativity: for a collection of dynamical wormholes and
black holes in a spacetime satisfying the null curvature condition, the maximin
area for a subset of the horizons (giving the largest area attained by the
minimal cross section of the multi-wormhole throat separating the subset from
its complement) is invariant under classical time evolution along the outermost
apparent horizons. The evolution can be completely general, including horizon
mergers and the addition of classical matter satisfying the null energy
condition. This theorem is the gravitational dual of entanglement conservation
and thus constitutes an explicit characterization of the ER=EPR duality in the
classical limit.Comment: 16 pages, 2 figure
Entanglement of Purification and Multiboundary Wormhole Geometries
We posit a geometrical description of the entanglement of purification for
subregions in a holographic CFT. The bulk description naturally generalizes the
two-party case and leads to interesting inequalities among multi-party
entanglements of purification that can be geometrically proven from the
conjecture. Further, we study the relationship between holographic
entanglements of purification in locally-AdS3 spacetimes and entanglement
entropies in multi-throated wormhole geometries constructed via quotienting by
isometries. In particular, we derive new holographic inequalities for
geometries that are locally AdS3 relating entanglements of purification for
subregions and entanglement entropies in the wormhole geometries.Comment: 23 pages, 12 figures; v2 added references; v3 fixed inequality
direction in Eq.(2), expanded discussion - reflects published versio
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