Scientific Series

In previous work it has been observed that the singularity structure of multi-loop scattering amplitudes in planar N=4
super-Yang-Mills theory is evidently dictated by cluster algebras. In my talk I will discuss the interplay between this mathematical
observation and the physical principle that the singularities of Feynman integrals are encoded in the Landau equations.

Effective field theories (EFT) are everywhere in particle physics. Given an EFT, the first question we ask is “what are all the operators consistent with the symmetries and degrees of freedom at a particular expansion order? In this talk I will show how this question can be attacked, and often answered, using an object called a Hilbert series.

I will discuss the recent progress on understanding scattering amplitudes in N=4 SYM beyond the planar limit. I will show that the singularity structure of these amplitudes is very similar to the planar amplitudes suggesting new hidden symmetries to be present in the complete N=4 SYM theory. I will also talk about the extension of this work to N=8 SUGRA by studying the on-shell diagrams in this theory as well as some of the properties of the integrands of loop amplitudes.

Topological insulators (TIs) are a recently discovered state of matter characterized by an “inverted” band structure driven by strong spin-orbit coupling. One of their most touted properties is the existence of robust "topologically protected" surface states.  I will discuss what topological protection means for transport experiments and how it can be probed using the technique of time-domain THz spectroscopy applied to thin films of Bi2Se3.  By measuring the low frequency optical response, we can follow their transport lifetimes as we drive these materials via chemical substitution through a quantum phase transition into a topologically trivial regime[1].  I will then discuss our work following the evolution of the response as a function of magnetic field from the semi-classical transport regime[2] to the quantum regime[3].  In the semi-classical regime, an anomalous increase of the transport scattering rate was observed at high field, which contribute from electron-phonon interaction[2].  In the highest quality samples[3,4], we observe a continuous crossover from a low field regime where the response is given by semi-classical transport and observed in the form of cyclotron resonance to a higher field quantum regime[3].  In the later case, we find evidence for Faraday and Kerr rotation angles quantized in units of the fine structure constant[3].  This quantized rotation angle can be seen as evidence for a novel magneto-electric of the TI’s surface e.g. the much heralded axion electrodynamics of topological insulators.  Among other aspects this give a purely solid-state measure of fine structure constant[3].

1. Wu, et al, Nat. Phys. 9, 410 (2013).

2. Wu, et al, Phy. Rev. Lett. 115, 217602  (2015).

3. Wu, et al, arXiv. 1603.04317 (2016)

4. Nikesh, et al, Nano. Lett. 15, 8245 (2015)

In this talk I will introduce recent research into quantum clocks of finite dimension, with the focus on their accuracy, as determined by their dimension, coherence, and power consumption.

I will present arguments to bound the synchronization time of any quantum clock as a function of its dimension. In addition, quantum coherence appears to be necessary to saturate these bounds, as the synchronization time of incoherent clocks is seen to have a worse bound. In addition, I will review simple proposals for autonomous clocks built out of thermal machines, and demonstrate that the power consumption of thermal clocks determines the limit of their accuracy. Finally, I will introduce an example of a finite quantum clock that is able to control any quantum operation up to a calculable accuracy, and discuss whether it represents a best case scenario for quantum clocks.

Winds are driven by the gradients of solar heating. Vertical gradients cause thermal convection on the scale of the troposphere depth (less than 10 km). Horizontal gradients excite motions on a planetary (10000 km) and smaller scales. Weather is mostly determined by the flows at intermediate scale (hundreds of kilometers). Where these flows get their energy from? The puzzle is that three-dimensional small-scale motions cannot transfer energy to larger scales while large-scale planar motions cannot transfer energy to smaller scales. In the talk, I'll describe experimental and observational data that suggest one possible resolution of this puzzle. I also describe some puzzling properties of two-dimensional turbulence including conformal invariance of statistics.

Planck's full-mission data, released in 2015, provides a high-resolution whole-sky polarization and temperature maps of the CMB and astrophysical components. I will talk about implications of Planck 2015 results for inflation, why cosmic dust is important, and what we are currently doing to study it. I will also highlight some tests of the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies we have done with observations made by the Planck satellite. I will show how simple map stacking can be used as a powerful statistical tool for studying polarized CMB and dust emission maps.

Quantum-critical strongly correlated electron systems are predicted to feature universal collision-dominated transport resembling that of viscous fluids. Investigation of these phenomena has been hampered by the lack of known macroscopic signatures of electron viscosity. Here we identify vorticity as such a signature and link it with a readily verifiable striking macroscopic DC transport behavior. Produced by the viscous flow, vorticity can drive electric current against an applied field, resulting in a negative nonlocal voltage. The latter may play the same role for the viscous regime as zero electrical resistance does for superconductivity. Besides offering a diagnostic which distinguishes viscous transport from ohmic currents, the sign-changing electrical response affords a robust tool for directly measuring the viscosity-to-resistivity ratio. Strongly interacting electron-hole plasma in high-mobility graphene affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.

Levitov and Falkovich, Nature Physics, 22 Feb 2016

Astrophysical observations spanning dwarf galaxies to galaxy clusters indicate that dark matter halos are less dense in their central regions compared to expectations from collisionless dark matter N-body simulations. Using detailed fits to dark matter halos of galaxies and clusters, we show that self-interacting dark matter may provide a consistent solution to the dark matter deficit problem across all scales, even though individual systems exhibit a wide diversity in halo properties. 

What are the bounds of the AdS/CFT correspondence? Which quantities in conformal field theory have simple descriptions in terms of classical anti-de Sitter spacetime geometry? These foundational questions in holography may be meaningfully addressed via the study of CFT correlation functions, which map to amplitudes in AdS. I will show that a basic building block in any CFT -- the conformal block -- is equivalent to an elegant geometric object in AdS, which moreover greatly streamlines and clarifies calculations of AdS amplitudes. By studying correlators with certain Lorentzian kinematics, one can constrain the space of consistent theories of AdS quantum gravity itself. In particular, by harnessing a recent bound on the rate of onset of chaos in thermal states, I will rule out the existence of certain classes of putative 2D CFTs and their 3D gravity duals, and argue that others exhibit signatures of Regge trajectories of string theory. This may be viewed as a novel, Lorentzian counterpart of the conformal bootstrap, relating dynamical constraints on the development of quantum chaos to the determination of the AdS/CFT landscape.

The mathematical notion of moonshine relates the theory of finite groups with that of modular objects. The first example, 'Monstrous Moonshine', was clarified in the context of two dimensional conformal field theory in the 90's. In 2010, interest in moonshine in the physics community was reinvigorated when Eguchi et. al. observed representations of the finite group M24 appearing in the elliptic genus of nonlinear sigma models on K3. In 2013, Cheng, Duncan, and Harvey provided a uniform construction of 23 new examples of moonshine, called 'umbral moonshine', of which M24 moonshine is a special case. 

In this talk, I will describe recent work studying the symmetries of certain Landau-Ginzburg orbifold theories that flow in the IR to c=6 N=(4, 4) superconformal field theories on the moduli space of K3 sigma models. We show that discrete symmetries of the UV theory implicate all 23 instances of umbral moonshine, not just M24 moonshine, in symmetries of K3 CFTs. I will then discuss a particular string theory compactification to three dimensions where we find a precise connection to all 23 umbral groups and type IIA string theory on K3.