This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
The Pauli exclusion principle is a constraint on the
natural occupation numbers of fermionic states. It has been suspected for
decades, and only proved very recently, that there is a multitude of further
constraints on these numbers, generalizing the Pauli principle. Surprisingly,
these constraints are linear: they cut out a geometric object known as a
polytope. This is a beautiful mathematical result, but are there systems whose
physics is governed by these constraints?
In one extreme, where the interactions
are sufficiently weak compared to the interactions, electrons form a “Fermi
liquid” – the state that accounts for the properties of simple metals. In the other extreme, where the interactions
are dominant, the electrons form various “Mott” insulating or “Wigner
crystalline” phases, often characterized by broken spatial and/or magnetic symmetries. Corresponding charge and/or magnetically
ordered insulating phases are common in nature.
The global warming
crisis is part of a bigger transformation in which humanity realizes that the
Earth is a finite system and that our population, energy usage, and the like
cannot continue to grow exponentially. While politics and economics pose the
biggest challenges, physicists are in a good position to help make this
transition a bit easier. After a quick review of the problems, we discuss a few
ways physicists can help.
Black holes are the elementary particles of gravity, the
final state of sufficiently massive stars and of energetic collisions. With a
forty-year long history, black hole physics is a fully-blossomed field which
promises to embrace several branches of theoretical physics. Here I review the
main developments in highly dynamical black holes with an emphasis on high
energy black hole collisions and probes of particle physics via superradiance.
Human monkeys are used to thinking about the problem of
choosing from a set of objects according to some desired, biased, probability
distribution. Just think about how you chose your partner(s). Even when it is
easy for you to do such a sampling, it can be difficult to do a quantum
sampling (Q-Sampling) of the same distribution. By Q-Sampling I mean the
creation of a coherent superposition of states of such objects whose amplitudes
are the (square roots of) of the specified distribution. In this talk I will
I'll explain a new connection between supersymmetric
gauge theories and the Yangian. The main result is that a twisted, deformed
version of the pure N=1 supersymmetric gauge theory is controlled by the
Yangian, in the same way that Chern-Simons theory is controlled by the quantum
group. This result is used to give an exact calculation, in perturbation
theory, of the expectation value of a certain net of n+m Wilson operators in
the deformed N=1 gauge theory. This expectation value coincides with the
The
holographic correspondence is a powerful duality between a quantum theory of
gravity and a quantum gauge theory in one lower space-time dimension. Higher
spin gravity theories, i.e. gravity theories that also contain (gauge) fields
of spins greater than 2, play a special role in holography. I will explain
consistent interacting higher spin gravity theories in anti-de Sitter space,
their duality with gauged conformal vector models, and their connection to
string theory.
I'll explain a new connection between supersymmetric
gauge theories and the Yangian. The main result is that a twisted, deformed
version of the pure N=1 supersymmetric gauge theory is controlled by the
Yangian, in the same way that Chern-Simons theory is controlled by the quantum
group. This result is used to give an exact calculation, in perturbation
theory, of the expectation value of a certain net of n+m Wilson operators in
the deformed N=1 gauge theory. This expectation value coincides with the
A
quantum spin liquid is a solid whose atoms have magnetic moments but, because
of quantum fluctuations, these moments fluctuate like a liquid even at zero
temperature. Two dimensional spin liquids have been suggested as a way to
produce high temperature superconductivity, and to build quantum computers. Just as helium is the only element which is a liquid at zero temperature,
2D spin liquids have been extremely difficult to find, despite decades of
effort, raising the question, do realistic spin liquids even exist?
The recent discovery
of the Higgs boson is a fundamental advance in particle physics. This talk
gives a theorist's perspective of the significance of this discovery. The Higgs
boson was proposed in the 1960s, but it is best understood in the context of
the quest to understand the weak interactions, which began with Fermi's theory
of weak interactions almost 80 years ago. This has led to three very different
paradigms for the structure of fundamental interactions at the TeV scale: