Numerical Study of a Bosonic Topological Insulator in Three Dimensions
Scott Geraedts California Institute of Technology
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Fundamental physics with muons
PIRSA:14100115 -
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Spinning Black Holes and the Membrane Paradigm
Robert Penna Massachusetts Institute of Technology (MIT)
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Cosmological Constraints on theories of Modified Gravity
Alexandre Barreira Durham University
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Superconformal Indices, AdS/CFT, and Cyclic Homologies
Richard Eager University of Tokyo
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Quantum Fields and Strings at Finite Coupling
Pedro Vieira Perimeter Institute for Theoretical Physics
PIRSA:14100050 -
Bulk Entanglement Spectrum: From Topological States to Quantum Criticality
Timothy Hsieh Perimeter Institute for Theoretical Physics
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The Minimal Modal Interpretation of Quantum Theory
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David Kagan University of Massachusetts Dartmouth
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Jacob Barandes Harvard University
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QQ-CHARACTERS, GAUGE THEORY and non-perturbative Dyson-Schwinger equations
Nikita Nekrasov Stony Brook University
PIRSA:14100066
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Numerical Study of a Bosonic Topological Insulator in Three Dimensions
Scott Geraedts California Institute of Technology
We construct a model which realizes a (3+1)-dimensional symmetry-protected topological phase of bosons with U(1) charge conservation and time reversal symmetry, envisioned by A. Vishwanath and T. Senthil [PRX 4 011016]. Our model works by introducing an additional spin degree of freedom, and binding its hedgehogs to a species of charged bosons. We study the model using Monte Carlo and determine its bulk phase diagram; the phase where the bound states of hedgehogs and charges condense is the topological phase, and we demonstrate this by observing a Witten effect. We also study the surface phase diagram on a (2+1)-dimensional boundary between the topological and trivial insulators. We find a number of exotic phases on the surface, including exotic superfluids, a phase with a Hall conductivity quantized to half the value possible in 2D, and a phase with intrinsic topological order. We also find a new bulk phase with intrinsic topological order. -
Disturbance in weak measurements and the difference between quantum and classical weak values
The role of measurement induced disturbance in weak measurements is of central importance for the interpretation of the weak value. Uncontrolled disturbance can interfere with the postselection process and make the weak value dependent on the details of the measurement process. Here we develop the concept of a generalized weak measurement for classical and quantum mechanics. The two cases appear remarkably similar, but we point out some important differences. A priori it is not clear what the correct notion of disturbance should be in the context of weak measurements. We consider three different notions and get three different results: (1) For a `strong' definition of disturbance, we find that weak measurements are disturbing. (2) For a weaker definition we find that a general class of weak measurements are non-disturbing, but that one gets weak values which depend on the measurement process. (3) Finally, with respect to an operational definition of the `degree of disturbance', we find that the AAV weak measurements are the least disturbing, but that the disturbance is still non-zero. -
Three-Point Function in N=4 SYM and Spin Vertex
In this talk I will explain how to compute three-point functions of N=4 SYM theory in the planar limit for tree level and one-loop in perturbation theory. First I will recall how to formulate the problem of computing the three-point function of operators with determined R-charges in the language of integrable spin chains. In the su(2) sector, the tree-level three point function can be obtained in terms of determinants, whose large R-charge limit can be taken explicitly. Then I will report a systematic method to compute the su(2) three point function at higher loops. In particular, we are able to take the semi-classical limit, and we can compare our result with the calculation from string theory. In the Frolov-Tseytlin limit we find a perfect match at one-loop. Finally I will present a new formalism of computing three-point functions called the spin vertex formalism, which is the weak coupling counter-part of the string vertex in the string field theory. I will describe how to construct the spin vertex and discuss its important properties. -
Fundamental physics with muons
PIRSA:14100115I will review applications of the muon as a probe for new phenomena. Topics to be discussed include the free muon decay and the determination of the Fermi constant; the anomalous magnetic moment of the muon; and searches for lepton flavor violation such as mu->e+gamma, mu->3e, and the muon-electron conversion, with special emphasis on the modification of the muon decay by the atomic binding. -
Schroedinger method as field theoretical model to describe structure formation
Cora Uhlemann Bielefeld University
We investigate large-scale structure formation of collisionless dark matter in the phase space description based on the Vlasov equation whose nonlinearity is induced solely by gravitational interaction according to the Poisson equation. Determining the time-evolution of density and velocity demands solving the full Vlasov hierarchy for the cumulants of the distribution function. In the presence of long-range interaction no consistent truncation is known apart from the dust model which is incapable of describing the formation of bound structures due to the inability to generate higher cumulants like velocity dispersion. Our goal is to find a simple ansatz for the phase space distribution function that approximates the full Vlasov distribution function and can serve as theoretical N-body double to replace the dust model. We present the Schroedinger method which is based on the coarse-grained Wigner probability distribution obtained from a wave function fulfilling the Schroedinger-Poisson equation as sought-after model. We show that its evolution equation approximates the Vlasov equation in a controlled way, cures the shell-crossing singularities of the dust model and is able to describe multi-streaming which is crucial for halo formation. This feature has already been employed in cosmological simulations of large-scale structure formation by Widrow & Kaiser (1993). We explain how the coarse-grained Wigner ansatz allows to calculate higher cumulants like velocity dispersion analytically from density and velocity in a self-consistent manner. On this basis we show that instead of solving the Vlasov-Poisson system one can use the Schrödinger method and solve the Schrödinger-Poission equation to directly determine density and velocity and all higher cumulants. As a first application we study the coarse-grained dust model, which is a limiting case of the Schrödinger method, within Eulerian and Lagrangian perturbation theory. -
Spinning Black Holes and the Membrane Paradigm
Robert Penna Massachusetts Institute of Technology (MIT)
There are about nine astrophysical black holes with measurements of the black hole's spin via the continuum fitting method. Several of these black holes drive powerful jets, which appear to extract the black hole's rotational energy. I will discuss the theory behind these observations, with a particular focus on the black hole membrane paradigm. The membrane paradigm is useful on a practical level for understanding black hole jets. However, it may also be related to fundamental physics through holography and AdS/CFT. This suggests new opportunities for interactions between fundamental physics and astrophysics. -
Cosmological Constraints on theories of Modified Gravity
Alexandre Barreira Durham University
Recently, research in cosmology has seen a growing interest in theories of gravity beyond General Relativity (GR). From an observational point of view, there are two main reasons for this. Firstly, the law of gravity has never been directly tested on scales larger than the Solar System. Hence, by understanding better the various signatures that different gravity models can leave on cosmological observables, one can improve the chances of identifying any departures from GR, or alternatively, extend the model's observational success into a whole new regime. Secondly, theories of modified gravity can arise also as an alternative to the cosmological constant (or any other form of dark energy) to explain the current accelerated expansion of the Universe. Using my results from suitably modified Boltzmann, N-body codes and semi-analytical models of structure formation, I will describe the way modified gravity models typically impact a series of cosmological observables. I will use two popular models as examples, which are known as Galileon and Nonlocal Gravity. In the Galileon model, the modifications to gravity on large scales are driven by nonlinear derivative interactions of a scalar field, which can nevertheless be suppressed in the Solar System by means of a mechanism known as Vainshtein screening. This model can provide a good fit to the latest CMB, BAO and SNIa data, although with different cosmological parameters than the standard LCDM model. Specifically, unlike LCDM, the Galileon model predicts nonzero neutrino masses (over 5sigma) and the constraints on the Hubble rate are compatible with its local determinations. The results from my N-body simulations and Halo Occupation Distribution analysis also show that the model can describe the measured clustering amplitude of Luminous Red Galaxies and that the screening mechanism can be very efficient in "hiding" the modifications to gravity on small scales. However, these results also show that the observational viability of the model may be under pressure due to the combined constraints derived from the sign of the ISW effect and from Solar System tests. In the Nonlocal model, the acceleration of the universe is driven by terms that involve the inverse of a derivative operator acting on curvature tensors. This model is also likely to pass large-scale structure constraints with the same flying colors as Galileon gravity, but the lack of a screening mechanism in this model makes it unclear on whether or not it is able to satisfy Solar System constraints. These steps I will describe for the cases of the Galileon and Nonlocal models can be viewed as guidelines for one to place constraints on other (or not yet invented) models of modified gravity. References: The results I will describe are based on the following papers: arXiv:1208.0600, arXiv:1302.6241, arXiv:1306.3219, arXiv:1308.3699, arXiv:1401.1497, arXiv:1404.1365, arXiv:1406.0485, arXiv:1408.1084 -
Superconformal Indices, AdS/CFT, and Cyclic Homologies
Richard Eager University of Tokyo
We explain how to obtain the spectrum of operators with protected scaling dimensions in a four-dimensional superconformal field theory from cyclic homology. Additionally, we show that the superconformal index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver. For quiver gauge theories which are dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein manifold with five-dimensional AdS space, the index is calculated both from the gauge theory and gravity viewpoints. We find complete agreement. Finally we show how to match the spectrum of protected operators on a supergravity compactification involving generalized complex geometry. -
Quantum Fields and Strings at Finite Coupling
Pedro Vieira Perimeter Institute for Theoretical Physics
PIRSA:14100050Gauge theories lie at the heart of our understanding of three of the four known forces in nature: the electromagnetic, weak and strong forces. Moreover, our best understood non-perturbative definition of a theory of quantum gravity is also given by a gauge theory. Yet, despite their absolutely central role in physics, gauge theories are still far from being tamed with our current theoretical tools. In this colloquium we shall explore the realm of quantum fields and strings at finite coupling and survey some of the exciting recent developments which are improving this state of affairs. The main character in our incursions will be a most symmetric gauge theory known as N=4 super Yang-Mills theory, often referred to as the harmonic oscillator of the twenty first century or, as it was most recently coined, as the Darth Vader theory. -
Bulk Entanglement Spectrum: From Topological States to Quantum Criticality
Timothy Hsieh Perimeter Institute for Theoretical Physics
A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce a partition of the system into two subsystems both of which extend throughout the bulk in all directions. The resulting bulk entanglement spectrum (BES) has a low-lying part that resembles the excitation spectrum of a bulk Hamiltonian, which allows us to probe a topological phase transition from a single wavefunction by tuning either the geometry of the partition or the entanglement temperature. As an example, this remarkable correspondence between topological phase transition and entanglement criticality is rigorously established for integer quantum Hall states. We also implement BES using tensor networks, derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase, and demonstrate that the AKLT wavefunction (and its generalizations) remarkably contains critical six-vertex (and in general eight-vertex) models within it. -
The Minimal Modal Interpretation of Quantum Theory
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David Kagan University of Massachusetts Dartmouth
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Jacob Barandes Harvard University
A persistent mystery of quantum theory is whether it admits an interpretation that is realist, self-consistent, model-independent, and unextravagant in the sense of featuring neither multiple worlds nor pilot waves. In this talk, I will present a new interpretation of quantum theory -- called the minimal modal interpretation (MMI) -- that aims to meet these conditions while also hewing closely to the basic structure of the theory in its widely accepted form. The MMI asserts that quantum systems -- whether closed or open -- have actual states that evolve along kinematical trajectories through their state spaces, and that those trajectories are governed by specific (if approximate) dynamical rules determined by a general new class of conditional probabilities, and in a manner that differs significantly from the de Broglie-Bohm formulation. The MMI is axiomatically parsimonious, leaves the usual dynamical content of quantum theory essentially intact, and includes only metaphysical entities that are either already a standard part of quantum theory or that have counterparts in classical physics. I will also address a number of important issues and implicit assumptions in the foundations community that I believe merit reconsideration and re-evaluation going forward. -
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QQ-CHARACTERS, GAUGE THEORY and non-perturbative Dyson-Schwinger equations
Nikita Nekrasov Stony Brook University
PIRSA:14100066We report on recent advances in understanding the non-local symmetries of quantum field theory, notably gauge theory. The symmetries relate topologically distinct sectors of the field space. We study these symmetries in some detail in the context of the BPS/CFT correspondence. We also introduce a notion of qq-characters, which generalize the q-characters of quantum affine algebras, introduced by E. Frenkel and N. Reshetikhin, and conjecturally are related to the (q, t)-characters introduced by H. Nakajima. We show that the qq-characters can be used to derive an infinite set of Dyson-Schwinger type relations which imply that the supersymmetric partition functions of four dimensional gauge theory (with surface operators) obey BPZ and KZB-type equations.