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Supersymmetric Sigma Model Geometry
Symmetry 2012, 4(3), 517-536; doi:10.3390/sym4030517

Supersymmetric Extensions of Non-Relativistic Scaling Algebras

1 Department of Physics, Ibaraki University, Mito 310-8512, Japan 2 Department of Physics, Kyoto University, Kyoto 606-8502, Japan
* Author to whom correspondence should be addressed.
Received: 3 July 2012 / Revised: 7 August 2012 / Accepted: 8 August 2012 / Published: 24 August 2012
(This article belongs to the Special Issue Supersymmetry)
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An exciting subject in string theory is to consider some applications of the AdS/CFT correspondence to realistic systems like condensed matter systems. Since most of such systems are non-relativistic, an anisotropic scaling symmetry with the general value of dynamical critical exponent z plays an important role in constructing the gravity duals for non-relativistic field theories. Supersymmetric extensions of symmetry algebras including the anisotropic scaling are very helpful to consider holographic relations accurately. We give a short summary on the classification of superalgebras with the anisotropic scaling as subalgebras of the following Lie superalgebras, psu(2,2|4), osp(8|4) and osp (8*|4), which appear in the study of AdS/CFT in type IIB string and M theories. It contains supersymmetric extensions of Schrödinger algebra and Lifshitz algebra.
Keywords: supersymmetry; non-relativistic limit; scale invariance; AdS/CFT supersymmetry; non-relativistic limit; scale invariance; AdS/CFT
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sakaguchi, M.; Yoshida, K. Supersymmetric Extensions of Non-Relativistic Scaling Algebras. Symmetry 2012, 4, 517-536.

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