Contact Geometry in Superconductors and New Massive Gravity

Abstract

The defining property of every three-dimensional ε-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we consider S 3 equipped with a contact structure together with an associated metric tensor such that the canonical generators of the contact distribution are null. The resulting Lorentzian metric is shown to be a vacuum solution of three-dimensional massive gravity. Moreover, by coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory.