Holographic correspondence in topological superconductors

Abstract

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.

4 pages

References in corpus (7)

• Spacetime Symmetries of the Quantum Hall Effect
• Thermal Hall Effect and Geometry with Torsion
• Low-energy effective theory in the bulk for transport in a topological phase
• Topological field theory and thermal responses of interacting topological superconductors
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• The CFT dual of AdS gravity with torsion
• Induced topological order at the boundary of 3D topological superconductors

Cited by in corpus (19)

• A Short Introduction to Topological Quantum Computation
• Emergent spacetime and gravitational Nieh-Yan anomaly in chiral $p+ip$ Weyl superfluids and superconductors
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• Probing topological superconductors with emergent gravity
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Hamiltonian approach to the torsional anomalies and its dimensional ladder
• Geometric description of the Kitaev honeycomb lattice model
• Geometric Model of Topological Insulators from the Maxwell Algebra
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• AdS/CFT Correspondence with a 3D Black Hole Simulator
• Specific heat of 2D interacting Majorana fermions from holography
• Nested Defects on the Boundary of Topological Superconductors
• Conformal energy currents on the edge of a topological superconductor
• Quantum geometric tensors from sub-bundle geometry
• Geometric and computational aspects of chiral topological quantum matter
• From topological to topologically massive gravity through the gauge principle