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Title: Topological insulators and superconductors from string theory

Abstract

Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the {theta} term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realizationmore » of topological insulators and superconductors in terms of holography (AdS/CFT).« less

Authors:
;  [1]
  1. Department of Physics, University of California, Berkeley, California 94720 (United States)
Publication Date:
OSTI Identifier:
21432447
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 82; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.82.086014; (c) 2010 American Institute of Physics; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANTI DE SITTER SPACE; CLASSIFICATION; D-BRANES; GAUGE INVARIANCE; HOLOGRAPHY; INTERACTIONS; PERIODICITY; QUANTUM FIELD THEORY; STRING MODELS; STRING THEORY; SUPERCONDUCTORS; SYMMETRY; TOPOLOGY; BRANES; COMPOSITE MODELS; EXTENDED PARTICLE MODEL; FIELD THEORIES; INVARIANCE PRINCIPLES; MATHEMATICAL MODELS; MATHEMATICAL SPACE; MATHEMATICS; M-THEORY; PARTICLE MODELS; QUARK MODEL; SPACE; VARIATIONS

Citation Formats

Ryu, Shinsei, Takayanagi, Tadashi, and Institute for the Physics and Mathematics of the Universe. Topological insulators and superconductors from string theory. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.086014.
Ryu, Shinsei, Takayanagi, Tadashi, & Institute for the Physics and Mathematics of the Universe. Topological insulators and superconductors from string theory. United States. doi:10.1103/PHYSREVD.82.086014.
Ryu, Shinsei, Takayanagi, Tadashi, and Institute for the Physics and Mathematics of the Universe. Fri . "Topological insulators and superconductors from string theory". United States. doi:10.1103/PHYSREVD.82.086014.
@article{osti_21432447,
title = {Topological insulators and superconductors from string theory},
author = {Ryu, Shinsei and Takayanagi, Tadashi and Institute for the Physics and Mathematics of the Universe},
abstractNote = {Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the {theta} term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).},
doi = {10.1103/PHYSREVD.82.086014},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 82,
place = {United States},
year = {2010},
month = {10}
}