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Niayesh Afshordi, Perimeter Institute
Trials and Tribulations of Aether
The tremendous empirical success of Einstein's relativity has pushed Aether into a chapter in the history books, for nearly a century. However, a phenomenologically consistent quantum mechanical treatment of gravity has motivated a revival of aether, by taming its UV-divergences, or the cosmological constant problem. Here I will outline the phenomenological implications of a physically motivated aether model. I will also discuss how aether could potentially evade traditional tests of Lorentz violation, through strong coupling. Stephon Alexander, Dartmouth College
Emergent Conformal Violation: Does Inflation Like Fundamental Scalar Fields?
We present a new model of inflation which does not rely on fundamental scalar fields. The theory is a conformally invariant gauge field theory minimally coupled to massless fermions. At the beginning of inflation, the conformal symmetry is dynamically broken by a BCS condensation of the fermions, leading to a spontaneously violation of conformal symmetry. A quasi de-Sitter inflationary regime is driven by the interaction between a homogenous plasma dynamo between the gauge, gravitational and condensate field. Unique observational consequences of this model are twofold :
(1) The sourcing of B-mode vorticity fluctuations in upcoming CMB powerspectra.
(2) A possible inflationary Baryogenesis mechanism connected to the initial conditions of inflation.
We end with a speculation of this model in the context of geodesically complete inflation and quantum gravity. Edward Anderson, Université Paris Diderot
Relationalism
I shall describe Relationalism, especially in the Leibniz-Mach-Barbour sense of the word and my variations on that theme. My presentation shall give five extensions to Barbour's work: (more or less) phase space, categorization, subsystems analysis, quantization, and physics as a propositional logic (`questions about physical systems'). I shall also briefly explain how some of Crane and Rovelli's ideas do fit within this scheme, whilst others are at odds with the LMB scheme, leaving one choosing options rather thanjust considering unions. I shall also present how scale-invariant and scaled relational particle models (the latter originally discovered by Barbour and Bertotti in 1982) can, in dimension 1 and 2, which suffice to toy-model many midisuperspace aspects of GR, be very generally solved at the following levels. 1) configuration space geometry following my fortuitous connection with Kendall's work in the statistical theory of shape involving the self-same space of shapes, and then the cone over this in the scaled case. 2) Conserved quantities and classical equations of motion. 3) Quantum equations of motion and their solutions. 4) Parallels of many Problem of Time strategies. I view this second paragraph as relevant not only by 4) but more widely by how it is a model of quantum background independence (BI), with BI being argued to be the other half to 'relativistic gravitation' in that gestalt entity known as General Relativity. Itzhak Bars, University of Southern California
Conformal Cosmology and Physics at Gravitational and Electroweak Scales
New techniques for obtaining the complete set of analytic solutions of the usual cosmological equations continue to shed new light on various aspects of cosmology. This approach, which was developed with a locally Weyl invariant formulation of gravity in 3+1 dimensions, was inspired by the 2T-physics formulation of all physics in 4+2 dimensions. I will first give a review of the general aspects of the analytic cosmological solutions, including recent work with Shi-Hung Chen, Paul Steinhardt and Neil Turok, on geodesic completeness through the singularity and the nature of the Big Crunch/Big Bang transition. Then I will include the full Standard Model, and discuss how the instability of the Higgs potential and the conditions for the electroweak phase transition develop slowly during cosmological evolution of the universe, thus understanding that the electroweak phase transition is not "spontaneous" and the Standard Model is not decoupled from gravity or cosmology. This scenario, which is currently being developed further, is the natural cosmological consequence of coupling the Standard Model to Gravity by imposing Weyl symmetry, a feature that is required if 2T-physics in 4+2 dimensions is considered as the starting point. There are no dimensionful parameters, not even the Newton constant. Emergent dimensionful scales are dynamical during the evolution of the universe. Steven Carlip, University of California, Davis
Two-dimensional Conformal Symmetry of Short-distance Spacetime
Evidence from several approaches to quantum gravity hints at the possibility that spacetime undergoes a "spontaneous dimensional reduction" at very short distances. If this is the case, the small scale universe might be described by a theory with two-dimensional conformal symmetry. I will summarize the evidence for dimensional reduction and indicate a tentative path towards using this conformal invariance to explore quantum gravity. Henrique de Andrade Gomes, University of California, Davis
The Theory of Shape Dynamics
Shape Dynamics is a theory dynamically equivalent to 3+1 vacuum General Relativity in a certain restriction of phase space. However, it has a different set of symmetries. It trades refoliation invariance, present in GR, for local 3-dimensional conformal invariance. Here we will review the rigorous construction of Shape Dynamics, the incorporation of matter and tractability issues of the model. We finish by mentioning interesting future prospects and open issues of the program.
Benjamin Grinstein, University of California, San Diego
Scale Without Conformal Invariance in Relativistic Quantum Field Theory
In 2-dim it is known that a unitary, well defined quantum field theory, if scale invariant must also be invariant under conformal transformations. Whether this is also true in dimensions higher than two has been an open question for decades. We have discovered renomalization group flows in 4-epsilon dimensions corresponding to scale but not conformal invariant theories. The flows correspond to limit cycles or ergodic behavior, neither of which had been reported in relativistic quantum field theories either. There seems to be a deep connection between scale without conformal invariance and this type of renormalization group behavior. We will present these results and list some of open questions, including the possibility of such behavior in integral dimensions. Sean Gryb, Utrecht University
2+1 gravity as a conformal gauge theory and some frontiers for Shape Dynamics
I will start by showing that gravity, with positive cosmological constant in 2+1 dimensions, can be formulated as a theory of dynamic conformal spatial geometry. Exploiting the isomorphism between the isometry group of de Sitter space in D+1 dimensions and the conformal group in D dimensions, I will reinterpret the Chern--Simons formulation of 2+1 gravity as a gauge theory of a conformal connection. In Cartan's generalization of geometry, this connection represents an evolving spatial geometry locally modeled off the conformal sphere. After a suitable phase space reduction, we obtain shape dynamics. This remodeling explains, in 2+1 dimensions, the remarkable success of the York procedure for solving the initial value problem of general relativity and the uniqueness of the shape dynamics Hamiltonian. I will finish by speculating about possible connections between this work and the general shape dynamics program with holographic renormalization, AdS/CFT, and Horava gravity. Petr Horava, University of California, Berkeley
The Multicritical Universe
This talk reviews the idea of quantum gravity with anisotropic scaling, and presents a scenario in which this theory of gravity is coupled to matter, described by the standard model or beyond.This "multicritical universe" scenario predicts systematic, energy-dependent, calculable Lorentz-violating corrections to the relativistic dispersion relations of matter. Viqar Husain, University of New Brunswick
Time and a Physical Hamiltonian for Quantum Gravity
I will describe an approach to the problem of time that uses dust as a time variable. The canonical theory is such that there is a true Hamiltonian with spatial diffeomorphisms as the only gauge symmetry. This feature, and the form of the Hamiltonian, suggest a model for non-perturbative quantum gravity that is computationally accessible using the formalism of loop quantum gravity. James Isenberg, University of Oregon
The Conformal Method and Solutions of the Einstein Constraint Equations: A Status Report
The Conformal Method (as well as the closely related Conformal Thin Sandwich Method) has proven to be a very useful procedure both for constructing and for parametrizing solutions of the Einstein initial data constraint equations, for initial data sets with constant mean curvature (CMC). Is this true for non CMC data sets as well? After reviewing the CMC results, we discuss what we know and don't know about non CMC initial data sets and the effectiveness of the Conformal Method in handling them. Tim Koslowski, Perimeter Institute
Doubly General Relativity
The symmetry principles of General Relativity and Shape Dynamics are both motivated by Mach's principle but implement different aspects: local relativity of clocks versus local relativity of rods. I will discuss how the two seemingly incompatible implied symmetry principles can be reconciled into a theory that implements both relativity principles as two distinct BRST transformations. I will briefly discuss what is needed to make use of this symmetry doubling in quantum theories. Renate Loll, Utrecht University
Towards Conformal Degrees of Freedom in CDT
TBA Joao Magueijo, Imperial College London
Is Nothing Sacred? The Cosmological Pay Off from Breaking Lorentz and Diffeormorphism Invariance
I show how the local Lorentz and/or diffeomorphism invariances may be broken by a varying c, softly or harshly, depending on taste. Regardless of the fundamental implications of such dramas, these symmetry breakings may be of great practical use in cosmology. They may solve the horizon and flatness problems. A near scale-invariant spectrum of fluctuation may arise, even without inflation. Distinct imprints may be left, teaching us an important lesson: our foundations may be flimsier than we like to think. Flavio Mercati, University of Nottingham
Shape Dynamics: Relativity Without Relativity
I review the best-matching construction, and the striking properties of a Jacobi-type action first introduced by Baierelein, Sharp and Wheeler. The simplest theories compatible with such an action principle must have a universal light-cone and gauge symmetry. I also describe the implementation of three-dimensional conformal symmetries on the basis of the BSW action, which gives a first-principles derivation of York's solution of the initial value problem in General Relativity. Godfrey Miller, University of Pennsylvania
The DBI Pseudo-Conformal Universe: Scale Invariance from Spontaneous Breaking of Conformal Symmetry
The pseudo-conformal scenario is an alternative to inflation in which the early universe is approximately described by a conformal field theory in Minkowski space. Crucially, the cosmological background spontaneously breaks the flat space so(4,2) conformal algebra down to its so(4,1) de Sitter subalgebra, causing conformal-weight-0 fields to acquire a scale invariant spectrum of perturbations. This framework is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. After reviewing the salient features of the model, I will describe a DBI realization of the pseudo-conformal scenario, in which scale-invariance is further protected by an additional shift symmetry acting on the weight-0 field. Shinji Mukohyama, Kavli Institute, IPMU
Cosmology and GR Limit of Horava-Lifshitz Gravity
TBA Kostas Skenderis, University of Amsterdam
Conformal Gravity and AdS/CFT
TBA Alexander Stottmeister, Institute for Theoretical Physics III, University of Erlangen-Nurnberg
On a partially Reduced Phase Space Quantisation of General Relativity Conformally Coupled to a Scalar Field
We comment on a certain partially reduced phase space quantisation of general relativity conformally coupled to a scalar field, and its extension to standard model matter fields. The partially reduced phase space is reached by trading the Hamiltonian constraint for the generator of local conformal transformations on all phase space variables, inspired by the ideas of shape dynamics, and constructing conformally invariant connection variables. Furthermore, we review this trading of symmetries from the gauge fixing/unfixing perspective, which is dual to the concept of a linking theory. Finally we point out possible applications and open problems. Gerard t'Hooft, Utrecht University
Conformal Gravity and Black Hole Complementarity
Hawking radiation is an observer-dependent phenomenon: observers who travel into a black hole do not perceive it but outside observers do. This implies that outside observers also perceive a space-time metric that differs from the metric perceived by an observer going in. Assuming causality to be a basic relation between spacetime points, one is led to believe that lightcones should not be observer dependent. This leaves the conformal factor as an observer-dependent variable. This picture seems to make sense. It implies that conformal symmetry must be exact, but spontaneously broken by the vacuum. One is led to questions concerning the conformal anomalies, and constraints on the matter interaction that one day might enable us to actually compute constants of nature such as the finestructure constant from first principles.
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