Holographic superconductor with multiple competing condensates

Abstract

Holography is a novel approach to modeling strongly interacting many-body systems. By reorganizing the quantum many-body problem into an equivalent problem in classical gravity, holography makes it relatively easy, for example, to study linear response and compute transport coefficients. These techniques have recently been used to build toy models of superconductivity known as "Holographic Superconductors". In this thesis, we will be applying these same holographic principles to a strongly-interacting superconducting system in which multiple condensates compete. In the gravitational description, our system begins with two non-interacting Abelian Higgs multiplets, each comprised of a vector and a charged scalar. This describes a system with two independent condensates. Coupling the scalars via a quartic interaction induces a competition between the two condensates, with a condensate of one operator suppressing or enhancing the other depending on the sign of the coupling.