Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
Jennifer Cano University of California System
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Format results
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On the role of the extra kinetic term coupling ƛ in classical Hořava-Lifshitz gravity
Luis Pires Radboud Universiteit Nijmegen
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Black holes without Lorentz symmetry
Thomas Sotiriou University of Nottingham
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Anomalies of discrete symmetries and Symmetry Protected Topological Phases
Anton Kapustin California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
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Noncommutative geometry and the symmetries of the standard model
Fedele Lizzi University of Naples Federico II
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The Case for an Alternative Cosmology
Jayant Narlikar IUCAA - The Inter-University Centre for Astronomy and Astrophysics
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John Paul Robinson: Art, Science and Myth
PIRSA:14050062 -
Physics, Logic and Mathematics of Time
Louis Kauffman University of Illinois at Chicago
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Group Field Theory in dimension 4 - ε
Sylvain Carrozza University of Burgundy
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Geometric inequalities for black holes
Sergio Dain Universidad Nacional de Cordoba
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Quantum thermalization and many-body Anderson localization
David Huse Princeton University
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Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
Jennifer Cano University of California System
The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at fillings 8 and 12 with experimentally-testable consequences. We also show examples for Abelian fractional quantum Hall states, the simplest examples being at filling fractions 8/7, 12/11, 8/15, 16/5. For all examples, we propose experiments that can distinguish distinct edge phases. Our results are summarized by the observation that edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, there are usually many stable fully chiral edge phases corresponding to the same bulk. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis also leads to a simple demonstration that all Abelian topological phases can be represented by a Chern-Simons theory parameterized by a K-matrix. -
On the role of the extra kinetic term coupling ƛ in classical Hořava-Lifshitz gravity
Luis Pires Radboud Universiteit Nijmegen
We study the classical constraint algebra of Hořava-Lifshitz gravity, where due to the breaking of 4d diffeomorphism symmetry, there is a new dimensionless coupling absent in GR and whose role is not yet clear. Starting from two apparently contradictory results, we show how the role of the extra coupling differs between the projectable and non-projectable versions of the theory. In particular, we see how in the latter, it gives rise to a non-trivial constraint algebra, akin to the conditions seen in the CMC gauge of GR. -
Black holes without Lorentz symmetry
Thomas Sotiriou University of Nottingham
Our current definition of what a black hole is relies heavily on the assumption that there exists a finite maximum speed of propagation for any signal. Indeed, one is tempted to think that the notion of a black hole has no place in a world with infinitely fast signal propagation. I will use concrete examples from Lorentz-violating gravity theories to demonstrate that this naive expectation is not necessarily true. -
Scattering of emerging excitations in Matrix Product States
Jutho Haegeman Ghent University
We review the formalism of matrix product states and one of its recent generalisations which allows to variationally determine the dispersion relation of elementary excitations in generic one-dimensional quantum spin chains. These elementary excitations dominate the low energy effective behaviour of the system. We discuss recent work where we show how we can also describe the effective interaction between these excitations – as mediated by the strongly correlated ground state – and how we can extract the corresponding S matrix. With these two ingredients, we can already build a highly non-trivial low-energy description of any microscopic Hamiltonian by assuming that higher order scattering processes are negligible. This allows to extract accurate information about the behaviour of the system under perturbations or at finite temperature, as we illustrate using the spin 1 Heisenberg model. -
Anomalies of discrete symmetries and Symmetry Protected Topological Phases
Anton Kapustin California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
There is a close connection between Symmetry Protected Topological Phases and anomalies: a surface of an SPT phase typically has a global symmetry with a nonvanishing 't Hooft anomaly which is canceled by the anomaly inflow from the bulk. This observation together with the known results about the classification of SPT phases suggest that anomalies are much more ubiquitous than thought previously and do not require chiral fermions We elucidate the physical mechanism of anomalies and give examples of bosonic theories with 't Hooft anomalies in various dimensions. -
Noncommutative geometry and the symmetries of the standard model
Fedele Lizzi University of Naples Federico II
I will describe Connes approach to the standard model based on spectral noncommutative geometry with particular emphasis on the symmetries. The model poses constraints which are satisfied by the standard model group, and does not leave much room for other possibilities. There is however a possibility for a larger symmetry (the ``grand algebra'') which may also be instrumental to obtain the correct mass of the Higgs. -
The Case for an Alternative Cosmology
Jayant Narlikar IUCAA - The Inter-University Centre for Astronomy and Astrophysics
This talk will describe the Quasi-Steady State Cosmology proposed in 1993 by Fred Hoyle, Geoffrey Burbidge and Jayant Narlikar. Starting with the motivation for this exercise, a formal field theoretic framework inspired by Mach’s principle is shown to lead to this model. The model is a generalization of the classical steady state model in the sense that it is driven by a scalar field which causes creation in explosive form. Such ‘minicreation events’ lead to a universe with a long term de Sitter expansion superposed with oscillations of shorter time scales. It is shown that this cosmology explains all the observed cosmological features and that there exist potential tests to distinguish between this cosmology and the standard big bang cosmology. -
John Paul Robinson: Art, Science and Myth
PIRSA:14050062Canadian glass artist and Renaissance man, John Paul Robinson, explores the mythic potential of science. Explaining that, “This is the idea that scientific discovery is changing our mythology by changing our understanding of the world and our place in it.” Backed with a firm understanding of the science he references, his sculptures poetically interpret such theoretical phenomena as wave particles, string mathematics and black holes. Most people, especially scientists see mythology and science as mutually exclusive and many believe that a scientific understanding of the world will eventually eliminate the need for myth. This idea is based on a misunderstanding as to what myth really is and it’s relationship to science. Myth is not superstition, fairy tail or lies nor is it truth, history or fact. Myth is Art. Myth is a picture, a story, a map; we use to navigate the world. Not the external material world but the world we all create and hold in our minds. In every human mind is a mythic picture of the world that provides the stage for all we experience. This picture not only helps us navigate our world but also performs the critical function of informing our sense of place and belonging within that world. Science cannot replace myth but it can inform it for mythology deals not with the mysteries generated by our ignorance of how the world works but by our understanding of how the world works. The mathematics of string theory is a powerful tool to describe the world but even physicists have to close their eyes and picture in their minds the world their equations are describing. The equation is pure logic and reason, but the picture of tiny strings playing the music that creates the universe is pure mythology. Award-winning glass artist and instructor John Paul Robinson was educated at the Georgian College of Arts and Technology in Barrie, Ontario, and the Ontario College of Art, where he subsequently taught for a number of years. His work has been exhibited in solo shows throughout Canada and the United States, in cities such as Montreal, Toronto and Chicago. Robinson’s works are held in the collections of The Museum of Civilization in Ottawa, Ontario, the Museum of American Glass in Millville, New Jersey and the Musée des Beaux-arts de Montréal, Québec. He has also created the Amber Archive, an annual participatory art project to communicate our existence and creative endeavours (by artists, designers and scientists) to beings millions of years in the future. -
Physics, Logic and Mathematics of Time
Louis Kauffman University of Illinois at Chicago
Consider discrete physics with a minimal time step taken to be
tau. A time series of positions q,q',q'', ... has two classical
observables: position (q) and velocity (q'-q)/tau. They do not commute,
for observing position does not force the clock to tick, but observing
velocity does force the clock to tick. Thus if VQ denotes first observe
position, then observe velocity and QV denotes first observe velocity,
then observe position, we have
VQ: (q'-q)q/tau
QV: q'(q'-q)/tau
(since after one tick the position has moved from q to q').
Thus [Q,V]= QV - VQ = (q'-q)^2/tau. If we consider the equation
[Q,V] = k (a constant), then k = (q'-q))^2/tau and this is recognizably
the diffusion constant that arises in a process of Brownian motion.
Thus, starting with the simplest assumptions for discrete physics, we are
lead to recognizable physics. We take this point of view and follow it
in both physical and mathematical directions. A first mathematical
direction is to see how i, the square root of negative unity, is related
to the simplest time series: ..., -1,+1,-1,+1,... and making the
above analysis of time series more algebraic leads to the following
interpetation for i. Let e=[-1,+1] and e'=[+1,-1] denote, as ordered
pairs, two phase-shifted versions of the alternating series above.
Define an operator b such that eb = be' and b^2 = 1. Regard b as a time
shifting operator. The operator b shifts the alternating series by one
half its period. Regard e' = -e and ee' = [-1.-1] = -1 (combining term by
term). Then let i = eb. We have ii = (eb)(eb) = ebeb = ee'bb = -1. Thus ii = -1
through the definition of i as eb, a temporally sensitive entity that
shifts it phase in the course of interacting with (a copy of) itself.
By going to i as a discrete dynamical system, we can come back to the
general features of discrete dynamical systems and look in a new way at
the role of i in quantum mechanics. Note that the i we have constructed is
already part of a simple Clifford algebra generated by e and b with
ee = bb = 1 and eb + be = 0. We will discuss other mathematical physical
structures such as the Schrodinger equation, the Dirac equation and the
relationship of a simple logical operator (generalizing negation) with
Majorana Fermions. -
Group Field Theory in dimension 4 - ε
Sylvain Carrozza University of Burgundy
Rank 3 tensorial group fields theories with gauge invariance condition appear to be renormalizable on dimension 3 groups such as SU(2), but also on dimension 4 groups. Building on an analogy with ordinary scalar field theories, I will generalize such models to group dimension 4 - ε, and discuss what this might teach us about the physically relevant SU(2) case. -
Geometric inequalities for black holes
Sergio Dain Universidad Nacional de Cordoba
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole (angular momentum, charge, mass and horizon area) satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. Also, variants of these inequalities are valid for ordinary bodies. In this talk I will review recent results in this subject. -
Quantum thermalization and many-body Anderson localization
David Huse Princeton University
Progress in physics and quantum information science motivates much recent study of the behavior of strongly-interacting many-body quantum systems fully isolated from their environment, and thus undergoing unitary time evolution. What does it mean for such a system to go to thermal equilibrium? I will explain the Eigenstate Thermalization Hypothesis (ETH), which posits that each individual exact eigenstate of the system's Hamiltonian is at thermal equilibrium, and which appears to be true for most (but not all) quantum many-body systems. Prominent among the systems that do not obey this hypothesis are quantum systems that are many-body Anderson localized and thus do not constitute a reservoir that can thermalize itself. When the ETH is true, one can do standard statistical mechanics using the `single-eigenstate ensembles', which are the limit of the microcanonical ensemble where the `energy window' contains only a single many-body quantum state. These eigenstate ensembles are more powerful than the traditional statistical mechanical ensembles, in that they can also "see" the quantum phase transition in to the localized phase, as well as a rich new world of phases and phase transitions within the localized phase.