Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter

Abstract

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.

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References in corpus (2)

• Topological Insulators
• Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

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• Disclinations in the geometric theory of defects
• Compatibility conditions of continua using Riemann-Cartan geometry
• Tilt induced vortical response and mixed anomaly in inhomogeneous Weyl matter
• A-geometrical approach to Topological Insulators with defects
• A geometric formulation of Schaefer's theory of Cosserat solids
• A supersymmetric spin current
• Interference effects and modified Born rule in the presence of torsion
• Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations