The Holographer’s Guide to Maxwell and Higgs

In the context of holography or gauge-gravity duality, boundary conditions of bulk fields play the fundamental and pivotal role to understand the nature of the dual field theory. The objective of this talk is to showcase the potential of mixed boundary conditions to accomplish the dynamical electromagnetism in the boundary theory, which is essential for the application of holography in real-world phenomena like magnetohydrodynamics, plasma physics, and superconductors. This talk will highlight two exemplary cases to provide a proof of concept. Firstly, a (3+1)-dimensional Einstein-Maxwell gravity theory with mixed boundary conditions will be demonstrated to yield results that perfectly align with relativistic magnetohydrodynamics in (2+1)-dimensions. Additionally, I will also illustrate the establishment of a bona-fide holographic superconductor using mixed boundary conditions, along with an exploration of its collective excitations and confirmation of the Anderson-Higgs mechanism.