Colloquium

Conformal Field Theory (CFT) describes the long-distance
dynamics of numerous quantum and statistical many-body systems. The
long-distance limit of a many-body system is often so complicated that
it is hard to do precise calculations. However, powerful new
techniques for understanding CFTs have emerged in the last few years,
based on the idea of the Conformal Bootstrap. I will explain how the
Bootstrap lets us calculate critical exponents in the 3d Ising Model
to world-record precision, how it explains striking relations between
magnets and boiling water, and how it can be applied to questions
across theoretical physics.

In this talk, I will focus on cosmologies that replace the big bang with a big bounce. I will explain how, in these scenarios, the large-scale structure of the universe is determined during a contracting phase before the bounce and will describe the recent development of the first well-behaved classical (non-singular) cosmological bounce solutions.

 Non-Fermi liquids are exotic metallic states which do not support well defined quasiparticles. Due to strong quantum fluctuations and the presence of extensive gapless modes near the Fermi surface, it has been difficult to understand universal low energy properties of non-Fermi liquids reliably.  In this talk, we will discuss recent progress made on field theories for non-Fermi liquids. Based on a dimensional regularization scheme which tunes the number of co-dimensions of Fermi surface, critical exponents that control scaling behaviors of physical observables can be computed in controlled ways. The systematic expansion also provides important insight into strongly interacting metals. This allows us find the non-perturbative solution for the strange metal realized at the antiferromagnetic quantum critical point in 2+1 dimensions and predict the exact critical exponents.

In recent years, precise cosmological measurements have provided strong evidence for new physics beyond the Standard Model, occurring both in the very early universe and also today.  In the near future, large-scale galaxy surveys will open another window on many different areas of physics, including tests of gravity, probes of dark energy, and cosmic inflation.  However, interpreting galaxy surveys presents new challenges, because galaxies are sensitive to astrophysics that are unimportant for the cosmic microwave background.  I will discuss how galaxies may be used to study cosmology, and will argue that the messy astrophysics in galaxies actually offers entirely new probes of fundamental physics.  I will illustrate this with 3 examples, related to inflation, neutrino masses, and the properties of dark matter.

I will argue that the standard model contains a rather strong hint that -- instead of being simply an ordinary continuous 4D manifold -- spacetime is actually the product of a 4D manifold and a certain discrete/finite 6D space (i.e. there are 6D discrete/finite "extra dimensions").  I will introduce this idea and the evidence for it in simple way, and then discuss various outstanding puzzles and future directions.

Tensor networks offer an efficient representation of many-body wave-functions in an exponentially large Hilbert space by exploiting the area law of ground state quantum entanglement. I will start with a gentle introduction to the tensor network formalism. Then I will describe its application to realizing Wilson's renormalization group directly on quantum lattice models (e.g. quantum spin chains), with emphasis on the RG fixed points corresponding to conformal field theories. We will see how to define both global and local scale transformations on the lattice in such a way that, intriguingly, conformal invariance can be tested (and conformal data extracted) right at the UV cut-off scale.

Scale invariant transfer matrices and Hamiltonians Abstract We investigate the possibility of strictly scale invariant transfer matrices in quantum spin chains based on a certain planar algebra, both as operators and as quadratic forms.

Recent explorations of the space of quantum field theories have provided novel topological and geometric information about this space. This voyage has resulted in the solution of some long-standing questions:  the computation of sought-after topological invariants (Gromov-Witten invariants) by a new physics-based approach, the first instance of exact correlation functions in a four-dimensional QFT and the unearthing of the action of dualities on the basic observables of three dimensional gauge theories.

Experimentalists are getting better and better at building qubits, but no matter how hard they try, their qubits will never be perfect.  In order to build a large quantum computer, we will almost certainly need to encode the qubits using quantum error-correcting codes and encode the quantum circuits using fault-tolerant protocols.  This will eventually allow reliable quantum computation even when the individual components are imperfect.  I will review the current state of the art of quantum fault tolerance and discuss progress towards answering the most important questions that will enable large fault-tolerant quantum computers.

Should we revisit the concept of space solely based on quantum mechanics?

Do we need a radically new physical principle to address the problem of quantum gravity?

In this talk I will adress these questions. I will review what are the central challenges one faces when trying to understand the theory of quantum gravity from first principles and focus on the main one which is non-locality.

I will present a collection of results and ideas that have been developed in the recent years that provides a radical new perspective on these issues.

One of the central concept I'll present is the idea that locality has to be made relative, and how this idea goes back to one of the founder of quantum mechanics: Max Born. I'll also explain how these new ideas remarkably force us to revisit the concept of space itself and propose a natural generalization that incorporate quantum mechanics in its fabric called modular space. I'll also sketch how these foundational ideas quite unexpectedly links with the most recent developments on the geometry of string theory, and generalized geometry.

Dark energy, the driver of the accelerated expansion of the universe, remains a conundrum. New physics may well be needed to explain it; from Lorentz invariance, this new physics should contain scalar fields, which should be straightforward to detect — so where are they? Physicists have now realized that scalar fields can hide from detection by three distinct screening mechanisms, which respectively rely on nonlinear features in the scalar’s kinetic energy, potential energy, or coupling to normal matter. These fields go by names such as galileons, chameleons, f(R) gravity, or symmetrons and range from theoretically well-motivated and natural to speculative. We will present new techniques to detect these particles, relying on interferometry with cold atoms in vacuum. The low density of such atoms compared to bulk matter avoids triggering some screening mechanisms, while the high sensitivity of the interferometer overcomes other screening mechanisms by brute force. We will show limits ruling out substantial regions of parameter space for chameleons and symmetrons [Science 349, 849 (2015)] and argue that an interferometer with 10,000 fold improved sensitivity will be able to search the gamut of screened scalar fields. A positive identification would revolutionize particle physics and cosmology, but even a null result would have important implications for our understanding of the dark sector.