Topological insulators and superconductors from string theory

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.086014· OSTI ID:21432447

Ryu, Shinsei; Takayanagi, Tadashi ^[1]

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1. Department of Physics, University of California, Berkeley, California 94720 (United States)

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).

• OSTI ID: 21432447
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 8; Other Information: DOI: 10.1103/PhysRevD.82.086014; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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