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"Quantum gravity"
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Quantum space : loop quantum gravity and the search for the structure of space, time, and the universe
Today we are blessed with two extraordinarily successful theories of physics. The first is Albert Einstein's general theory of relativity, which describes the large-scale behaviour of matter in a curved spacetime. This theory is the basis for the standard model of big bang cosmology. The discovery of gravitational waves at the LIGO observatory in the US (and then Virgo, in Italy) is only the most recent of this theory's many triumphs. The second is quantum mechanics. This theory describes the properties and behaviour of matter and radiation at their smallest scales. It is the basis for the standard model of particle physics, which builds up all the visible constituents of the universe out of collections of quarks, electrons and force-carrying particles such as photons. The discovery of the Higgs boson at CERN in Geneva is only the most recent of this theory's many triumphs. But, while they are both highly successful, these two structures leave a lot of important questions unanswered. They are also based on two different interpretations of space and time, and are therefore fundamentally incompatible. We have two descriptions but, as far as we know, we've only ever had one universe. What we need is a quantum theory of gravity. Approaches to formulating such a theory have primarily followed two paths. One leads to String Theory, which has for long been fashionable, and about which much has been written. But String Theory has become mired in problems. In this book, Jim Baggott describes : an approach which takes relativity as its starting point, and leads to a structure called Loop Quantum Gravity. Baggott tells the story through the careers and pioneering work of two of the theory's most prominent contributors, Lee Smolin and Carlo Rovelli. Combining clear discussions of both quantum theory and general relativity, this book offers one of the first efforts to explain the new quantum theory of space and time\"-- Provide by publisher.
Book
Edge modes of gravity. Part I. Corner potentials and charges
A
bstract
This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different formulations of gravity provide non-trivial representations of different sectors of the corner symmetry algebra, and ii) set the foundations of a new proposal for states of quantum geometry as representation states of this corner symmetry algebra. In this first paper we explain how different formulations of gravity, in both metric and tetrad variables, share the same bulk symplectic structure but differ at the corner, and in turn lead to inequivalent representations of the corner symmetry algebra. This provides an organizing criterion for formulations of gravity depending on how big the physical symmetry group that is non-trivially represented at the corner is. This principle can be used as a “treasure map” revealing new clues and routes in the quest for quantum gravity. Building up on these results, we perform a detailed analysis of the corner pre-symplectic potential and symmetries of Einstein-Cartan-Holst gravity in [1], use this to provide a new look at the simplicity constraints in [
2
], and tackle the quantization in [
3
].
Journal Article
Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
A
bstract
Motivated by the prospect of constraining microscopic models, we calculate the exact one-loop corrected de Sitter entropy (the logarithm of the sphere partition function) for every effective field theory of quantum gravity, with particles in arbitrary spin representations. In doing so, we universally relate the sphere partition function to the quotient of a quasi-canonical bulk and a Euclidean edge partition function, given by integrals of characters encoding the bulk and edge spectrum of the observable universe. Expanding the bulk character splits the bulk (entanglement) entropy into quasinormal mode (quasiqubit) contributions. For 3D higher-spin gravity formulated as an sl(
n
) Chern-Simons theory, we obtain all-loop exact results. Further to this, we show that the theory has an exponentially large landscape of de Sitter vacua with quantum entropy given by the absolute value squared of a topological string partition function. For generic higher-spin gravity, the formalism succinctly relates dS, AdS
±
and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.
Journal Article
The story of collapsing stars : black holes, naked singularities, and the cosmic play of quantum gravity
\"This book journeys into one of the most fascinating intellectual adventures of recent decades - understanding and exploring the final fate of massive collapsing stars in the universe. The issue is of great interest in fundamental physics and cosmology today, from both the perspective of gravitation theory and of modern astrophysical observations. This is a revolution in the making and may be intimately connected to our search for a unified understanding of the basic forces of nature. According to the general theory of relativity, a massive star that collapses catastrophically under its own gravity when it runs out of its internal nuclear fuel must give rise to a space-time singularity. Such singularities are regions in the universe where all physical quantities take their extreme values and become arbitrarily large. The singularities may be covered within a black hole, or visible to faraway observers in the universe. Thus, the final fate of a collapsing massive star is either a black hole or a visible naked singularity. We discuss here recent results and developments on the gravitational collapse of massive stars and possible observational implications when naked singularities happen in the universe.\"--Back cover.
Book
Generalized entropy for general subregions in quantum gravity
A
bstract
We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the
G
N
→ 0 limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we argue that the algebra is a type II von Neumann factor. To do so in the former case we introduce a model of an observer living in the region; in the latter, the ADM Hamiltonian effectively serves as an observer. In both cases the entropy of states on which this algebra acts is UV finite, and we find that it agrees, up to a state-independent constant, with the generalized entropy. For spatially compact regions the algebra is type II
1
, implying the existence of an entropy maximizing state, which realizes a version of Jacobson’s entanglement equilibrium hypothesis. The construction relies on the existence of well-motivated but conjectural states whose modular flow is geometric at an instant in time. Our results generalize the recent work of Chandrasekaran, Longo, Penington, and Witten on an algebra of operators for the static patch of de Sitter space.
Journal Article
The quantum gravity dynamics of near extremal black holes
A
bstract
We study the quantum effects of Near-Extremal black holes near their horizons. The gravitational dynamics in such backgrounds are closely connected to a particle in
AdS
2
with constant electric field. We use this picture to solve the theory exactly. We will give a formula to calculate all correlation functions with quantum gravity backreactions as well as the exact Wheeler-DeWitt wavefunction. Using the WdW wavefunction, we investigate the complexity growth in quantum gravity.
Journal Article
Edge modes of gravity. Part II. Corner metric and Lorentz charges
A
bstract
In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential. We start by performing a detailed decomposition of the various geometrical quantities appearing in BF theory and tetrad gravity. This provides a new decomposition of the symplectic potential of BF theory and the simplicity constraints. We then show that the dynamical variables of the tetrad gravity corner phase space are the internal normal to the spacetime foliation, which is conjugated to the boost generator, and the corner coframe field. This allows us to derive several key results. First, we construct the corner Lorentz charges. In addition to sphere diffeomorphisms, common to all formulations of gravity, these charges add a local
sl
(2
,
ℂ) component to the corner symmetry algebra of tetrad gravity. Second, we also reveal that the corner metric satisfies a local
sl
(2
,
ℝ) algebra, whose Casimir corresponds to the corner area element. Due to the space-like nature of the corner metric, this Casimir belongs to the unitary discrete series, and its spectrum is therefore quantized. This result, which reconciles discreteness of the area spectrum with Lorentz invariance, is proven in the continuum and without resorting to a bulk connection. Third, we show that the corner phase space explains why the simplicity constraints become non-commutative on the corner. This fact requires a reconciliation between the bulk and corner symplectic structures, already in the classical continuum theory. Understanding this leads inevitably to the introduction of edge modes.
Journal Article
Liouville quantum gravity — holography, JT and matrices
A
bstract
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of
SL
(2
,
ℝ), a connection we develop in some detail. For the case of the (2
, p
) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large
p
limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large
p
limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.
Journal Article
Evidence for a sublattice weak gravity conjecture
A
bstract
The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index
sublattice
of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal particle exists at
every
lattice site, including an example in which the lightest charged particle is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it implies that if a gauge group with very small coupling
e
exists, then the fundamental gravitational cutoff energy of the theory is no higher than ∼
e
1/3
M
Pl
.
Journal Article