My research focuses on superconductivity and quantum phase transitions in nuclear matter at high densities, as occur in neutron stars, for example. At ordinary low densities, quarks are tightly confined into the familiar nuclei from the standard table of elements. As densities increase, however, nuclear matter undergoes several phase transitions ultimately dissociating into constituent quarks and gluons forming a strongly interacting quantum liquid, or quark-gluon plasma, through a phenomenon known as asymptotic freedom. There are presently many open questions regarding the structure of matter between these extremes of low and high densities.
From a technical standpoint, one attractive aspect of studying nuclear matter at low-temperatures is that these regimes are amenable to effective models of quantum chromodynamics, the quantum field theory that describes the strong interaction between quarks and gluons. These models are generically referred to as four-fermion theories since the gluon degrees of freedom are absorbed into point-like four-quark vertices. Presently, I am using analytical methods that incorporate spin-charge separation for quarks into superconducting four-fermion models in order to resolve the low-temperature microphysics of the meson-diquark phase transition. In particular, I am interested in understanding how topological structures such as skyrmions, vortices, and instantons might be involved in the meson-diquark transition, as well as quantum phase transitions in more general field theories. Ordinarily, topological objects are too heavy to play a significant role at low temperatures, yet their effects may be strong at quantum critical points when competing orders exhibit unusually rich topologies.
More fundamentally, I am interested in connections between quantum field theories and theories of gravity known as holographic or gauge-gravity dualities: the notion that certain quantum mechanical theories in flat space-time contain theories of gravity in one higher dimension hidden within the subtleties of their mathematical structure, and conversely that Einstein’s field equations have something to say about quantum mechanics. This is undoubtedly one of the great discoveries of late twentieth century physics. I am particularly interested in gaining a deeper understanding of quantum gravity by elucidating the topological sectors of certain quantum field theories and studying the emergent dual gravity theories.