Low Energy Challenges for High Energy Physicists
I will discuss the enhancement of space-time symmetries to Lorentz (rotation) invariance at the renormalization group fixed points of non-relativistic (anisotropic) field theories. Upon describing examples from the condensed matter physics, I will review the general argument for the stability of the infrared fixed points with the enhanced symmetry. Then I will focus on unitary field theories in (1+1) space-time dimensions which are invariant under translations, isotropic scale transformations and satisfy the requirement that the velocity of signal propagation is bounded from above.
In an incoherent metal, transport is controlled by the collective diffusion of energy and charge rather than by quasiparticle or momentum relaxation. We explore the possibility of a universal bound D \gtrsim \hbar v_F^2 /(k_B T) on the underlying diffusion constants in an incoherent metal. Such a bound is loosely motivated by results from holographic duality, the uncertainty principle and from measurements of diffusion in strongly interacting non-metallic systems.
Due to the current search of Majorana fermions, the physics of two-dimensional identical fermions with short-range p-wave interactions is of considerable interest. My talk will be about the effective theory of a chiral p+ip fermionic superfluid at zero temperature. This theory naturally incorporates the parity and time reversal violating effects such as the Hall viscosity and the edge current. I will present some applications of this theory such as the linear response to external electromagnetic and gravitational fields and the density profile of an isolated vortex.
Recently developed techniques allow imaging of electronic quantum matter directly at the atomic scale. I will introduce the basic principles and describe the set of observables available from these techniques. As examples, I will survey visualization of exotic forms of electronic quantum matter including heavy fermions, quantum critical electrons, topological surface states, electronic liquid crystals, and high temperature superconductors.
Studies of relativistic matter in strong magnetic fields attracted a lot of attention in recent years. Such studies are primarily motivated by the phenomenology of compact stars, the evolution of the Early Universe, and the physics of relativistic heavy ion collisions. Additionally, the outcomes of such research result in deeper understanding of a large class of novel condensed matter materials (e.g., graphene and Dirac semimetals. I will review recent surprises, ideas, and the progress made in understanding physical properties of relativistic matter in strong magnetic fields.
I will outline a path by which a semi-classical geometry obeying Einstein's equations emerges holographically from elementary quantum mechanical objects undergoing local dynamics. The key idea is that entanglement between the quantum degrees of freedom leads to the emergence of a dynamical geometry, that entanglement is the fabric of spacetime. Furthermore, although important technical challenges remain, I will argue that the conceptual ideas are in place.
I will review the development in understanding Nambu–Goldstone bosons in quantum many-body systems. Particular emphasis will be put on two topics of my recent work: spontaneous breaking of spacetime symmetries and construction of topological effective Lagrangians.
In this talk I will discuss the analogies between high energy scattering of nucleons and Fermi Liquid theory. In particular I will elucidate the relation between the rapidity renormalization group utilized in such observables as transverse momentum distribution and the effect of Von-Hove singularities on the low energy properties of metals.
We study the problem of metals near a quantum critical point using a local Wilsonian effective field theory of Fermi surface fermions coupled to massless boson (i.e. order parameter) fields, in particular in a large N limit where the boson is matrix-valued. We focus on regions of parameter space where the boson dresses the fermions into a non-Fermi liquid while the bosons are approximately controlled by the Wilson-Fisher fixed point.