Scientific Series

When performing numerical simulation of many-body systems we work with the goal of computing some set of averaged observables.  This process has a weakness in that, when our simulation is complete, we have no ability to determine what was the key physics that gave our result.  In this talk, I'll give a simple example, a gap in a single-particle density of states, and explain how we can use two-particle quantities to recover key 'hidden' information.  I'll then back up these claims with numerical results for the 2D Hubbard model.  For the second half of my talk I'll hope to keep your attention by introducing a parallel but MUCH more whimsical idea, unparticle physics. I'll at least TRY to explain what an unparticle is and how it might impact strongly correlated condensed matter systems.

There seem to be no good examples of UV complete theories that have low-lying massive higher spin states isolated by a large gap, despite the relative ease of constructing effective field theories describing such states.  We discuss constraints from analytic dispersion relations and subluminality of eikonal scattering that may help to explain this and provide insight into the possible interactions of massive higher spins.

First I will introduce the concept of the shadow of a black hole and what it means for the shadows of two observers to be degenerate. I will then present
our results showing that no continuous
degenerations exist between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass. Therefore an observer can, by measuring the black holes shadow, in principle determine the angular momentum and the charge of the black hole under observation, as well as his radial distance from the black hole and his angle of elevation above the equatorial plane.

CHIME is a new interferometric telescope at radio frequencies 400-800 MHz.The mapping speed (or total statistical power) of CHIME is among the largestof any radio telescope in the world, and the technology powering CHIME could be used to build telescopes which are orders of magnitude more powerful.This breakthrough sensitivity has the power to revolutionize radio astronomy, but meeting the computational challenges will require breakthroughs on the algorithmic side.  I'll give a status update on CHIME, with an emphasis on new algorithms developed at Perimeter to search for fast radio bursts (FRB's) and pulsars.

I will introduce our recent proposal that the state of the universe does *not* spontaneously violate CPT. Instead, the universe before the Big Bang is the CPT reflection of the universe after the bang. Phrased another way, the universe before the bang and the universe after the bang may be re-interpreted as a universe/anti-universe pair, created from nothing. CPT selects a unique vacuum state for the QFT on such a spacetime, which leads to a new perspective on the cosmological baryon asymmetry, and a new explanation for the observed dark matter abundance. In particular, if we assume that the matter fields in the universe are described by the standard model of particle physics (including right-handed neutrinos), we predict that one of the heavy neutrinos is stable, and that its density automatically matches the observed dark matter density if its mass is 4.8 x 10^8 GeV. Among other predictions, we have: (i) that the three light neutrinos are majorana; (ii) that the lightest of these is exactly massless; and (iii) that there are no primordial long-wavelength gravitational waves. I will mention connections to the strong CP problem and the arrow of time. (Based on arXiv:1803.08928 and arXiv:1803.08930, with Kieran Finn and Neil Turok.)

In the first part of the seminar I will give a short review of the frame-independent formulation of Newtonian gravity, called Newton-Cartan Gravity, and explain why there is a renewed interest into non-relativistic gravity in general.  In the second part I will discuss, as a particular application,  a recent proposal for an Effective Field Theory describing a massive spin-2 mode (the so-called GMP mode) in the Fractional Quantum Hall Effect.

This project examines the structure of a certain category of representations of a Lie algebra called Whittaker modules. Whittaker modules generalize highest weight modules, and the structure of the category is similar to that of Bernstein-Gelfand-Gelfand’s category O. In particular, Whittaker modules have finite length composition series and all irreducible Whittaker modules appear as quotients of standard Whittaker modules, which are generalizations of Verma modules. Using the localization theory of Beilinson-Bernstein, one obtains a beautiful geometric description of Whittaker modules as twisted sheaves of D-modules on the associated flag variety. I use this geometric setting to develop an algorithm for computing the multiplicities of irreducible Whittaker modules in the composition series of standard Whittaker modules. This algorithm establishes that the multiplicities are determined by parabolic Kazhdan-Lusztig polynomials.

Starting from the well known Laplace-Runge-Lenz vector of the Kepler problem, I will introduce a notion of dynamical (hidden)
symmetries. These are genuine phase space symmetries that stand in contrast to the more familiar symmetries of the configuration space
discussed in truncated versions of Noether's theorem. Proceeding to a relativistic description, I will demonstrate that such symmetries -- encoded
in the so called Killing-Yano tensors -- play a crucial role in the study of rotating black holes described by the Kerr geometry. Even more remarkably, I will show that one such special symmetry is enough to guarantee complete integrability of particle and light motion in general rotating black hole spacetimes in an arbitrary
number of spacetime dimensions. Recent developments on the separability of test fields in these spacetimes will also be discussed.

Diamond anvil cells and shock techniques now permit the study of matter under multimegabar (i.e. several hundred GPa) pressures. The properties of matter in this pressure regime differ drastically from those known at 1 atm. Just how different physics and chemistry are at high pressure and the role that a chemical intuition for bonding and structure can have in understanding matter at high pressures will be explored in this lecture. I will discuss in detail an overlapping hierarchy of responses to increased density, consisting of (a) squeezing out van der Waals space (for molecular crystals); (b) increasing coordination; (c) decreasing the bond length of covalent bonds and the size of anions; and (d) an extreme regime of electrons moving off atoms and new modes of correlation. Examples of the startling chemistry and physics that emerge under such extreme conditions will alternate in this account with qualitative chemical ideas about the bonding involved.

The space-based gravitational wave detector LISA may be able to detect gravitational waves from a first order phase transition at the electroweak scale. Acoustic waves produced during the transition are largely responsible for the resulting signal. I will present results from a large campaign of simulations studying such phase transitions, determining the spectral shape of the gravitational wave power spectrum with unparalleled accuracy. Measuring a cosmological stochastic background could place constraints on the phase transition parameters, such as the nucleation rate and temperature, and therefore provide important information about physics beyond the Standard Model. However, better understanding of the source, as well as the underlying theories of physics beyond the Standard Model, is required before the launch of LISA. I will outline how this understanding can be developed.

In this talk we will review our physical proposal, with D. Persson and R. Volpato, to understand the genus zero property of monstrous moonshine. The latter was proven by Borcherds in 1992 by brute-force computation but has since resisted a conceptual understanding. We embed the Monster VOA of Frenkel-Lepowsky-Meurman into a heterotic string compactification and use physical arguments, i.e. T-dualities and decompactification limits, to understand the genus zero property. We find that the Monster Lie algebra (a Generalized, or Borcherds-Kac-Moody algebra) acts as a sort of "algebra of BPS states". We also sketch an analogous proposal, with S. Harrison and R. Volpato, for Conway moonshine using the type II string. Along the way we construct a new super Borcherds-Kac-Moody algebra on which the Conway group acts faithfully and prove its (twisted) denominator identities, which should be identified with BPS state counts in our string theory. 

Already in their early papers, Kosterlitz and Thouless envisaged the melting of solids by the unbinding of the topological defects associated with translational order: dislocations. Later it was realized that the resulting phases have translational symmetry but rotational rigidity: they are liquid crystals.

We consider the topological melting of solids as a zero-temperature quantum phase transition. In a generalization of particle-vortex duality, the Goldstone modes of the solid, phonons, map onto gauge bosons which mediate long-range interactions between dislocations. The phase transition is achieved by a Bose-Einstein condensation of dislocations, restoring translational symmetry and destroying shear rigidity. The dual gauge fields become massive due to the Anderson-Higgs mechanism. In this sense, the liquid crystal is a "stress superconductor".

We have developed this dual gauge field theory both in 2+1D, where dislocations are particle-like and phonons are vector bosons, and 3+1D where dislocations are string-like and phonons are Kalb-Ramond gauge fields. Focussing mostly on the theoretical formalism, I will discuss the relevance to recent experiments on helium monolayers, which show evidence for a quantum hexatic phase.

References:

2+1D : Physics Reports 683, 1 (2017)

3+1D : Physical Review B 96, 1651115 (2017)