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, Dbranes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting lowenergy effective field theories realized by two parallel Dbranes, we establish a onetoone correspondence between the Ktheory classification of topological insulators/superconductors and Dbrane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the WessZumino term of the Dbranes gives rise to a gauge field theory of topological nature, such as ones with the ChernSimons 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 higherdimensional extensions. Increasing the number of Dbranes naturally leads to a realizationmore »
 Authors:

 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 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANTI DE SITTER SPACE; CLASSIFICATION; DBRANES; 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; MTHEORY; 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, Dbranes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting lowenergy effective field theories realized by two parallel Dbranes, we establish a onetoone correspondence between the Ktheory classification of topological insulators/superconductors and Dbrane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the WessZumino term of the Dbranes gives rise to a gauge field theory of topological nature, such as ones with the ChernSimons 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 higherdimensional extensions. Increasing the number of Dbranes 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 = {05562821},
number = 8,
volume = 82,
place = {United States},
year = {2010},
month = {10}
}