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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.