Scientific Series

Painlevé equations can be obtained both from time-dependent classical Hamiltonian systems and from isomonodromic deformation problems. These realizations lead to a precise matching between Painlevé equations and Hitchin systems associated to four-dimensional N=2 SQCD as well as Argyres-Douglas theories. Long-time analysis of the Painlevé Hamiltonians dynamics allows to extract the unrefined "instanton" partition function for these theories at all strong-coupling points

The T2K experiment studies neutrino properties by producing a beam of muon neutrinos and sending them 295 km across Japan to the Super-Kamiokande detector. En route, neutrinos undergo a transmutation known as “neutrino oscillations” wherein they can transition to two other species or flavours, electron and tau neutrinos. Starting in 2014, T2K has run with an antineutrino beam to study the corresponding antineutrino oscillations and the possibility that a  complex phase in the neutrino mass and flavour mixing may lead to differences in neutrino and antineutrino oscillations. Such a difference may provide a critical clue into how our universe came to be dominated by matter.  I will present the latest results from an analysis of T2K neutrino and antineutrino data taken through 2016 along with other recent results from other experiments, and discuss their implications for our understanding of neutrinos.

For a finite group G, a G-gerbe over a space B can be thought of as a fiber bundle over B with fibers the classifying orbifold BG. Hellerman-Henriques-Pantev-Sharpe studied conformal field theories on G-gerbes. Given a G-gerbe Y-> B, they constructed a disconnected space \widehat{Y} endowed with a locally constant U(1) 2-cocycle c. They conjectured that a CFT on Y is equivalent to a CFT on \widehat{Y} twisted by the "B-field" c. In this talk, I plan to explain the constructions in this conjecture and the mathematical side of the story, in particular the viewpoints from noncommutative geometry and Gromov-Witten theory. This is based on joint work with Xiang Tang.

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.

We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d (2,0) type J theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of JJ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of JJ type. We can obtain the Schur and Hall-Littlewood index of these theories by computing the vacua character of the corresponding chiral algebra.

Lack of fine tuning in effective field theory does not ensure that a particular scenario is natural or even realizable in a UV complete theory of quantum gravity. Large field axion inflation appears natural from the effective field theory perspective, but I argue that it is tuned from a quantum gravity perspective. The argument is based on the Weak Gravity Conjecture (WGC), a conjectural universal feature of quantum gravity that is present in all known string theory examples. In the process, I highlight recent progress in understanding the WGC and related conjectures about the charged spectrum of quantum gravity and discuss other potential applications, both formal and phenomenological.

It has long been wondered to what extent the observable properties of an inhomogeneous universe will be measurably different from a corresponding FLRW model. Here, we use tools from numerical relativity to study the properties of photons traversing an inhomogeneous universe. We evolve the full, unconstrained Einstein field equations for a spacetime containing dust, with a spectrum of long-wavelength density perturbations similar to the observed one. We then integrate the optical scalar equations along paths through this numerical spacetime, with all paths terminating at an observer situated similarly to ourselves, and construct the resulting Hubble diagrams.

I will talk about some connections among the GKZ (introduced by Gelfand-Kapranov-Zelevinsky) hypergeometric series, orbifold singularities of the system, and chain integrals in some geometry.  The GKZ hypergeometric series appeared in some very interesting contexts including arithmetic geometry, enumerative geometry and mathematical physics in the last few decades. I will report some new geometric realizations and interpretations of them.

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study local quantum many-body systems at low energies. 

In this talk, I will describe how a tensor network representation of a quantum many-body ground state also encodes, in a natural way, another quantum many-body state whose properties must be related to the ground state in a systematic way. One can apply this tensor network state correspondence to the multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a one dimensional (1D) quantum lattice system to obtain a quantum many-body state of a 2D hyperbolic quantum lattice, whose boundary is the original 1D lattice. I propose that this bulk/boundary correspondence could potentially be a candidate implementation of the holographic correspondence of String theory on a lattice using the MERA.

For the MERA representation of a critical ground state I will show how the critical properties can be obtained from the corresponding bulk state, in particular, illustrating how point-like boundary operators are identified with extended operators in the bulk. I will also describe the entanglement and correlations in the bulk state, present numerical results that illustrate that the bulk entanglement may depend on the boundary critical charge, and describe how the bulk state can be described in terms of "holographic screens". If the boundary state has a global symmetry, the corresponding bulk state has a local gauge symmetry (described by the same group). In fact, the bulk state decomposes in terms of spin networks as they appear in lattice gauge theory, where they describe the gauge-invariant sector of the theory (here, the bulk). This decomposition also reveals entanglement between gauge degrees of freedom in the bulk, which are dual to a global symmetry at the  boundary, and remaining bulk degrees of freedom which may potentially include gravitational degrees of freedom in a holographic interpretation of the MERA.

I discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. I review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. I describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system. If time permits I will comment on the link to Brownian quantum circuits and tensor networks.