skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1];  [2];  [1]
  1. School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT (United Kingdom)
  2. (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. 2016. "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 = 2016,
month = 9
}
  • The general correlator of composite operators of N=4 supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states.
  • The general correlator of composite operators of N=4 supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states. (c) 2000 The American Physical Society.
  • A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d+1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS{sub d+2}, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS{sub 3}. We also compare the entropy computed in AdS{sub 5}xS{sup 5} with that of the free N=4 super Yang-Mills theory.
  • To gain insight into how bulk locality emerges from the holographic conformal field theory (CFT), we reformulate the bulk-to-boundary map in as local a way as possible. In previous work, we carried out this program for Lorentzian anti-de Sitter (AdS), and showed the support on the boundary could always be reduced to a compact region spacelike separated from the bulk point. In the present work the idea is extended to a complexified boundary, where spatial coordinates are continued to imaginary values. This continuation enables us to represent a local bulk operator as a CFT operator with support on a finitemore » disc on the complexified boundary. We treat general AdS in Poincare coordinates and AdS{sub 3} in Rindler coordinates. We represent bulk operators inside the horizon of a Banados-Teitelboim-Zanelli (BTZ) black hole and we verify that the correct bulk two-point functions are reproduced, including the divergence when one point hits the BTZ singularity. We comment on the holographic description of black holes formed by collapse and discuss locality and holographic entropy counting at finite N.« less
  • No abstract prepared.