Colloquium

I will give an overview of the causal set approach to quantum gravity, and what makes this "fork in the road" distinct from other approaches.  Motivated by deep theorems in Lorentzian geometry, causal set theory (CST) posits that the underlying fabric of spacetime is  atomistic and encoded in a locally finite partially ordered set. In  the continuum  approximation,  the partial order corresponds to the causal structure, and the cardinality to the conformal factor.  Together, these give the approximate continuum geometry.  Lorentz invariance emerges as a consequence, but brings with it a certain  "non-locality”, which distinguishes CST  from other approaches in an essential way. It also makes the  reconstruction of spacetime geometry from the causal set particularly challenging.  I will describe some of the progress we have made in this geometric reconstruction program. I will then describe a particular formulation of CST dynamics inspired by the continuum path integral and discuss what we have learnt so far and where it is taking us. 

There is a long tradition of formulating Quantum Theory in an operational manner.  In one version of this a circuit is formed by wiring together operations. Each operation has knob settings and outcomes (lights flashing, detectors clicking, ..).  The question raised and answered in this colloquium is whether we can do the same for General Relativity.  There are hurdles that have to be overcome to do this - in particular, we need to define a diffeomorphism invariant notion of operations, identify what the knob settings and outcomes are, and what the wiring corresponds to.   In this colloquium I will provide an outline of how to formulate General Relativity like this providing a possibilistic calculus (we can calculate whether operationally described situations are possible or not).  This provides the beginnings of an operational approach to the problem of Quantum Gravity.  This talk is based on arxiv:1608.06940.  

The observed deviations from the laws of gravity of Newton and Einstein in galaxies and clusters can logically speaking be either due to the presence of unseen dark matter particles or due to a change in the way gravity works in these situations. Until recently there was little reason to doubt that general relativity correctly describes gravity in all circumstances. In the past few years insights from black hole physics and string theory have lead to a new theoretical framework in which the gravitational laws are derived from the quantum entanglement of the microscopic information that is underlying space-time. An essential ingredient in the derivation is of the Einstein equations is that the vacuum entanglement obeys an area law, a condition that is known to hold in Anti-de Sitter space due to the work of Ryu and Takayanagi. We will argue that in de Sitter space due to the positive dark energy, that the microscopic entanglement entropy also contains also a volume law contribution in addition to the area law. This volume law contribution is related to the thermal properties of de Sitter space and leads to a total entropy that precisely matches the Bekenstein-Hawking formula for the cosmological horizon. We study the effect of this extra contribution on the emergent laws of gravity, and argue that it leads to a modification compared to Einstein gravity. We provide evidence for the fact that this modification explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

 I will present several studies showing a surprising pattern. Not only can preschoolers learn abstract higher-order principles from data, but younger learners are actually better at inferring unusual or unlikely principles than older learners and adults. This pattern also holds for children in Peru and in Headstart programs in Oakland, California. I relate this pattern to computational ideas about search and sampling, to evolutionary ideas about human life history, and to neuroscience findings about the negative effects of frontal control on wide exploration. My hypothesis is that our distinctively long, protected human childhood allows an early period of broad hypothesis search, exploration and creativity, before the demands of goal-directed action set in.

The modeling of pulsar radio and gamma-ray emission suggests that in order to interpret the observations one needs to understand the field geometry and the plasma state in the emission region. In recent years, significant progress has been achieved in understanding the magnetospheric structure in the limit of abundant plasma supply. However, the very presence of dense plasma everywhere in the magnetosphere is not obvious. Even the region where the observed emission is produced is subject to debate. To address this from first principles, we constructed global kinetic simulations of pulsar magnetospheres using relativistic Particle-in-Cell codes, which capture the physics of plasma production and particle acceleration. In this talk I will describe how plasma is produced in magnetospheres of pulsars and show that effects of general relativity are crucial for the activity of pulsars with low inclination angles. I will present modeling of high-energy lightcurves, calculated self-consistently from particle motion in the pulsar magnetosphere. I will also show evidence that observed radio emission is powered by non-stationary discharge at the polar cap. Finally, I will argue that giant radio pulses in the Crab are produced by coherent plasma currents, which appear at the interfaces of merging plasmoids in the current sheet beyond the light cylinder.

Over the past several years, our understanding of topological electronic phases of matter has advanced dramatically.   A paradigm that has emerged is that insulating electronic states with an energy gap fall into distinct topological classes.   Interfaces between different topological phases exhibit gapless conducting states that are protected topologically and are impossible to get rid of.   In this talk we will discuss the application of this idea to the quantum Hall effect, topological insulators,  topological superconductors and the quest for Majorana fermions in condensed matter.   We will then show that similar ideas arise in a completely different class of problems.    Isostatic lattices are arrays of masses and springs that are at the verge of mechanical instability.   They play an important role in our understanding of granular matter, glasses and other 'soft' systems.  Depending on their geometry, they can exhibit zero-frequency 'floppy' modes localized on their boundaries that are insensitive to local perturbations.   The mathematical relation between this classical system and quantum electronic systems reveals an unexpected connection between theories of hard and soft matter.

The existence of a deconfined quantum-critical point [1] between the standard antiferromagnet
and a valence-bond solid in 2D S=1/2 quantum magnets has been controversial, in part due to
anomalous finite-size scaling behaviors observed in quantum Monte Carlo simulations interpreted by some as signs of a first-order transition. I will discuss a new finite-size scaling hypothesis in which a scaling function of two divergent length scales [the standard correlation length and a length-scale related to an emergent U(1) symmetry of the valence-bond solid] has a limiting form implying unconventional finite-size scaling behaviors, while maintaining conventional scaling in the thermodynamic limit [2]. This proposal goes beyond the standard scenario of a dangerously irrelevant perturbation as a source of the second length scale in, e.g., classical 3D clock models. Quantum Monte Carlo simulations of the J-Q model (a spin-1=2 Heisenberg model extended with certain multi-spin interactions) are in full agreement with the proposed scaling form, suggesting that deconfined quantum-criticality is an even richer phenomenon than initially imagined. Since finite temperature T plays the role of a finite imaginary-time dimension in quantum systems, the anomalous scaling behavior impacts also the scaling in the quantum-critical \fan" at T > 0. This is also observed in the J-Q model.

[1] H. Shao, W. Guo, and A. W. Sandvik, Science 352, 213 (2016).
[2] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, M. P. A. Fisher, Science 303, 1490 (2004).

An overview will be given of recently discovered connection between asymptotic symmetries in general relativity  and soft theorems in quantum field theory together with their implications for the black hole information paradox.

I will first show that a number of persistent astrophysical puzzles, including missing pulsars in the galactic center, fast radio bursts, the abundance of r-process elements, and the type Ia supernova progenitor problem, may all be an emerging signature of dark matter. I will address some theoretical implications and new astrophysical phenomena -- for example "quiet kilonovae" and "r-process donuts" -- associated with this dark matter. Then, I will describe a newly discovered effect, that dark matter crashing into neutron stars warms them to infrared temperatures detectable with the Thirty Meter, European Extremely Large, and James Webb Space telescopes.

Dark matter is all around us, however its particle physics nature is still mysterious. Searches for dark matter have largely focused on candidates with weak scale interactions to the standard model particles, the so-called WIMP paradigm. However, the parameter space of the WIMP paradigm is becoming increasingly constrained by both the LHC and direct detection experiments. Another possibility that is well motivated both theoretically and observationally is to have a dark sector connected with the visible one via a mediator whose coupling to the visible one is tiny. In this talk, based on my own work, I will discuss models in this direction and how to search for signals from the dark sector using various experiments including particle accelerators, dark matter direct detection experiments, cosmic ray experiments, and cosmic microwave background observation.