Emergent supersymmetry and holographic non-Fermi liquid

Abstract

Understanding dynamics of strongly coupled quantum field theories is an important problem in both condensed matter physics and high energy physics. In condensed matter systems, interacting quantum field theories can arise either at a critical point, or in a finite region of a parameter space. In the former case, massless modes arise as a result of fine tuning of external parameters, while, in the latter case, massless modes are protected by topology and/or symmetry. In this talk, I will discuss two examples in 2+1 dimensions (one for each case) where one can understand strong coupling physics nonperturbatively. In the first example, a lattice model which describes a superconducting phase transition will be discussed. In this model, a superconformal symmetry dynamically emerges at the quantum critical point and one can predict non-trivial critical exponents using the enlarged symmetry, even though there is no underlying supersymmetry in the microscopic model. In the second example, I will discuss about a 2+1 dimensional non-relativistic quantum field theory which is dual to a gravitational theory in the AdS4 background with a charged black hole. The spectral function of a fermion field exhibits an interesting non-Fermi liquid behavior, that is, all momentum points inside the Fermi surface are critical and the gapless modes are defined in a critical Fermi ball in the momentum space.