Chern-Simons Theory and Wilson Loops in the Brillouin Zone

Abstract

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the 6 dimensional phase space, where the physical space defects play the role of topological D-branes.

arXiv comment14 pages, 2 figures

References in corpus (30)

• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• The space group classification of topological band insulators
• Dynamical Axion Field in Topological Magnetic Insulators
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Knot Invariants and Topological Strings
• Helical Metal Inside a Topological Band Insulator
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Stability of Fermi Surfaces and K-Theory
• Fermi Surface Topological Invariants for Time Reversal Invariant Superconductors
• Electronic thermal conductivity and the Wiedemann-Franz law for unconventional superconductors
• Twisted equivariant matter
• Protected boundary states in gapless topological phases
• Topological Classification and Stability of Fermi Surfaces
• Topological surface states in nodal superconductors
• Types of topological surface states in nodal noncentrosymmetric superconductors
• Time-reversal invariant topological superconductivity in doped Weyl semimetals
• Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators
• Topological field theory and thermal responses of interacting topological superconductors
• Gauge Symmetry and Gravito-Electromagnetism
• A Five Dimensional Generalization of the Topological Weyl Semimetal
• Dynamical Axion Field in a Magnetic Topological Insulator Superlattice
• Electromagnetic and thermal responses in topological matter: topological terms, quantum anomalies and D-branes
• Unified Topological Response Theory for Gapped and Gapless Free Fermions

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