Scientific Series

In this first of two lectures, intended to be a pedagogical introduction, I will review the quantum field theory origin of anomalies starting with the more familiar example of the axial anomaly in QED, emphasizing the infrared effects and the appearance of a two-particle massless state, similar to a Cooper pairing in superconductor, associated with both the axial and conformal anomalies in two and four dimensions. In both cases the effective action of the anomaly is non-local, but may be expressed in a local form by the introduction of a bosonic field, which one can verify becomes a bona fide propagating quantum field in its own right. At finite chiral chemical potential this boson is a chiral density wave, a gapless pseudo-scalar collective excitation of the Fermi surface of a dissipationless chiral superfluid, analogous to the Goldstone-Nambu boson of spontaneous symmetry breaking. In the limit of vanishing chiral background the boson is a chiral collective mode of the Dirac vacuum itself, which therefore supports an axion-like boson excitation with a two-photon coupling, arising directly from the axial anomaly.

 

Despite much theoretical effort, there is no complete theory of the “strange” metal phase of the high temperature 

superconductors, and its linear-in-temperature resistivity. This phase is believed to be a strongly-interacting metallic 

phase of matter without fermionic quasiparticles, and is virtually impossible to model accurately using traditional

perturbative field-theoretic techniques. Recently, progress has been made using large-N techniques based on the 

solvable Sachdev-Ye-Kitaev (SYK) model, which do not involve expanding about any weakly-coupled limit. I will 

describe constructions of solvable models of strange metals based on SYK-like large-N limits, which can reproduce  

some of the experimentally observed features of strange metals and adjoining phases. These models, and further 

extensions, could possibly pave the way to developing a controlled theoretical understanding of the essential building 

blocks of the electronic state in correlated-electron superconductors near optimal doping.

Violations of Bell inequalities have traditionally been used to refute a local-realistic description of the world. Not surprisingly, under the assumption that the world is quantum, they can be used to certify quantum devices. What is surprising is that in some cases this characterisation turns out to be (almost) complete, i.e.~we can determine (almost) everything about the devices and this phenomenon is known as self-testing of quantum systems. Although the first self- testing results can be traced back to the works of Tsirelson published in the 80's, the topic has remained largely unknown until the seminal work of Mayers and Yao in 1998. It has received further exposure with the advent of device-independent quantum cryptography to which it is closely connected. In this talk I will give a brief introduction to the topic of self-testing and discuss some recent developments, e.g.~robust self-testing, weak self-testing, self-testing of entangled measurements, self-testing of high-dimensional systems or self-testing in prepare-and-measure scenarios.

A key prediction of the Lambda CDM framework of structure formation is that a host halo containing a Milky Way sized disk galaxy should contain hundreds of thousands of sub-dwarf galaxy mass dark matter subhalos. Devoid of stars, these substructures remain undetected. Detecting them will not only corroborate the existence of dark matter but also give crucial information on the particle nature of dark matter and how they cluster at small scale. Cold stellar streams originate when globular clusters are tidally disrupted in the Milky Way potential. Gravitational encounters with dark matter subhalos will perturb these streams' density. I will present a novel method of probing the fundamental nature of dark matter by statistically analyzing the power spectrum of the stream density. I will discuss the uncertainties that the known baryonic structures such as the Galactic bar, the spiral arms, the Galactic population of giant molecular clouds and globular clusters can impart. Understanding their effects will be crucial for deciding whether a particular stream can be used to probe dark matter substructures.  

We discuss some algebraic quantum field theory (AQFT) ingredients that should be useful in defining a tensor network describing a Lorentzian space-time.

We look into toy models that approximate Minkowski space and show how Lorentz boosts are approximately recovered, and obtain Rindler modes that can be compared with the entanglement spectrum. 

We make connections of these approximations of Lorentz boosts with the corner transfer matrices in integrable models, and comment on the discrete realization of the Reeh-Schlieder theorem that governs entanglement in a Hilbert space with lower bounded energy. 

One can associate to any finite graph Q the skew-symmetic Kac-Moody Lie algebra g_Q. While this algebra is always infinite, unless Q is a Dynkin diagram of type ADE, g_Q shares a lot of the nice features of a semisimple Lie algebra. In particular, the cohomology of Nakajima quiver varieties associated to Q gives a geometric representations of g_Q. Encouraged by this story, one could hope to define the Yangian of g_Q, for general Q, as a subalgebra of the algebra of endomorphisms of cohomology of quiver varieties. In fact there are two approaches to doing this: firstly via the stable envelope construction of Maulik and Okounkov, secondly via the preprojective Hall algebra of Schiffmann and Vasserot. Via another Hall algebra construction, due to Kontsevich and Soibelman, and work of myself and Meinhardt on BPS Lie algebras, these approaches turn out to be more or less the same. In showing this we show that the correct Lie algebra of endomorphisms associated to Q is cohomologically graded, with zeroeth piece the old Kac-Moody Lie algebra - the best way to build a (Borcherds) Lie algebra out of Q is directly from geometric representation theory.

I discuss the canonical degrees of freedom of metric Einstein gravity on a null surface. The constraints are interpreted as conservation equations of a boundary current. Gravitational fluxes are identified, and the Hamiltonians of diffeomorphism symmetry are discussed. Special attention is given to the role of a modification of the phase space at the boundary of the null surface. Based on 1802.06135 with Laurent Freidel.

Despite considerable effort, magic state distillation remains one of the leading candidates to achieve universal fault-tolerant quantum computation. However, when analyzing magic state distillation schemes, it is often assumed that gates belonging to the Clifford group can be implemented perfectly. In many current quantum technologies, two-qubit Cliffords gates are amongst the noisiest components of quantum computers. In this talk I will present a new scheme for preparing magic states with very low overhead that uses flag qubits. I will then compare our scheme to leading magic state distillation methods and show that the overhead can be reduced by orders of magnitude.

The two-point functions <O^n(x) Obar^n(y)> for generator O of Coulomb branch chiral rings in D=4 N=2 SCFT will be determined universally to all orders in 1/n by the theory's a-anomaly.
The calculation will be done using the method of large-charge expansion presented in [1706.05743]; the absence of F-terms in the (R-charge)^(-1) expansion of the effective action ensures this universality.
I will also comment on the non-universal and non-perturbative corrections to the two-point functions whose leading piece was numerically shown to go as O(exp(-sqrt(n))).  

While the term “wide-field telescope” might sound like an oxymoron, a strong argument can be made that wide-field instruments lie behind much of the success of Canadian astronomy. Furthermore, despite the large size of the optical-IR community in Canada, this success has been made possible by considering multiple wavelength windows, from gamma to radio, and access to a suite of facilities. Over the past two decades, through a pair of 10-year Long Range Plans, Canadian astronomy has carefully structured its facility access, to ensure, as best as can be reasonably hoped, that the community maintains access to world-leading facilities. I’ll summarize the progression of the community vision on wide-field astronomy, highlighting successes and some missteps. As we head towards the creation of the 3rd Canadian Long Range Plan for astronomy, I’ll also present some personal views on what scientific leadership means and the challenges that it presents for a smaller country (at least in the G7 sense!) like Canada.

Three dimensional fracton phases are new type of phases featuring exotic excitations called fractons. They are gapped point-like excitations constrained to move in sub-dimensional space. In this talk, I will present the gapped fracton topological order discovered in exact solvable models and gapless fracton phase described by U(1) symmetric tensor gauge theories. Their relation with ordinary topological ordered phase would be discussed in detail. Particularly, the fracton topological order exhibited in an exact solvable model called X-cube model can be constructed by coupling toric code layers. And it can also be obtained from a particular rank-2 symmetric tensor gauge theory called scalar charge theory by Higgs mechanism and partial confinement transition.