Hydrodynamical description of strongly coupled
In modern language, hydrodynamics is an effective field theory in which the long-lived fundamental degrees of freedom are (almost) conserved currents, such as charge and heat currents. This is the correct effective field theory to describe strongly coupled systems, wherein there are no well-defined microscopic particle-like degrees of freedom, and the only long-lived modes are conserved currents dictated by the symmetries of the system. I employ the powerful tools of hydrodynamics to construct effective field theories useful for describing strongly coupled electronic materials, such as high-temperature superconductors.
Conformal field theories and their perturbations around the critical point
Conformal field theories constitute a highly specialized category of Quantum Field Theories characterized by their symmetry under scale transformations. In the realm of Statistical Physics, they prove particularly valuable as they delineate the critical point of second-order phase transitions, where the system’s correlation length diverges, reinstating scale invariance. I employ a blend of analytical techniques, known as Conformal Perturbation Theory, alongside numerical Monte Carlo simulations, to perturb conformal field theories away from their conformal points. This approach grants insights into the behavior of physical systems in the proximity of a second-order phase transition.
The Gauge/Gravity duality posits a relationship between specific strongly coupled regimes of ordinary quantum field theories and classical (i.e., weakly coupled) theories of gravity in at least one higher dimension. It represents a novel and highly intriguing method for translating challenging quantum field theory problems into more manageable classical gravitational ones. My primary focus lies in utilizing this tool to analyze certain states of condensed matter that remain incompletely understood, including Unconventional Superconductors and the Fractional Quantum Hall Effect.
Daniel Keith Brattan