# 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.

- Authors:

- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT (United Kingdom)
- (Netherlands)

- Publication Date:

- OSTI Identifier:
- 22617376

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFORMAL INVARIANCE; HOLOGRAPHY; MAJORANA FERMIONS; QUANTUM FIELD THEORY; SUPERCONDUCTORS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Palumbo, Giandomenico, E-mail: giandomenico.palumbo@gmail.com, Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, and Pachos, Jiannis K..
```*Holographic correspondence in topological superconductors*. United States: N. p., 2016.
Web. doi:10.1016/J.AOP.2016.05.005.

```
Palumbo, Giandomenico, E-mail: giandomenico.palumbo@gmail.com, Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, & Pachos, Jiannis K..
```*Holographic correspondence in topological superconductors*. United States. doi:10.1016/J.AOP.2016.05.005.

```
Palumbo, Giandomenico, E-mail: giandomenico.palumbo@gmail.com, Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, and Pachos, Jiannis K.. Thu .
"Holographic correspondence in topological superconductors". United States.
doi:10.1016/J.AOP.2016.05.005.
```

```
@article{osti_22617376,
```

title = {Holographic correspondence in topological superconductors},

author = {Palumbo, Giandomenico, E-mail: giandomenico.palumbo@gmail.com and Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht and Pachos, Jiannis K.},

abstractNote = {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.},

doi = {10.1016/J.AOP.2016.05.005},

journal = {Annals of Physics},

number = ,

volume = 372,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}