Many-body systems with a conserved $U(1)$ current in $(2+1)$ dimensions may be probed by weakly gauging this current and studying correlation functions of magnetic monopole operators in the resulting dynamical gauge theory. We study such monopole correlations in holographic liquids with fundamental flavor, where the monopole operator is dual to a magnetically charged particle in the bulk. In charge-gapped phases, the monopole operator is expected to condense. We show that this condensation is holographically dual to the capping off of the bulk flavor brane and compute the monopole condensate. We argue that from the lower-dimensional point of view, this may be understood as a simple example of confinement of a gauge field in the bulk. In a compressible finite-density phase, we present a novel calculation of the monopole correlation in space and time: the correlation is power law in time but Gaussian in space due to interaction with the background charge density.

• Received 24 October 2014

DOI:https://doi.org/10.1103/PhysRevD.91.106001