Contact Geometry in Superconductors and New Massive Gravity

Abstract

The defining property of every three-dimensional $\epsilon$-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and $\eta$-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. As an example we analyse $S^3$ 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 para-contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory.

References in corpus (13)

• The Black Hole in Three Dimensional Space Time
• Massive Gravity in Three Dimensions
• On Eta-Einstein Sasakian Geometry
• The Cotton tensor in Riemannian spacetimes
• Birkhoff's Theorem for Three-Dimensional AdS Gravity
• Ricci solitons in three-dimensional paracontact geometry
• Using 3D Stringy Gravity to Understand the Thurston Conjecture
• Para-Sasakian geometry in thermodynamic fluctuation theory
• Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear sigma-model
• Thurston Geometries from Eleven Dimensions
• Contact metric three manifolds and Lorentzian geometry with torsion in six-dimensional supergravity
• Contact polarizations and associated metrics in geometric thermodynamics
• Electromagnetic fields from contact forms

Cited by in corpus (6)

• Thurston Geometries in Three-Dimensional New Massive Gravity
• Self-gravitating solutions in Yang-Mills-Chern-Simons theory coupled to 3D massive gravity
• Gravitational Waves from Thurston Geometries
• Light propagation through optical media using metric contact geometry
• Brief Note on Thurston Geometries in 3D Quadratic Curvature Theories
• The geometry of induced currents in two dimensional media