Supersymmetric Extensions of Non-Relativistic Scaling Algebras

Abstract

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.

SUSY properties of warped AdS3

“…Later, in section 3, we show how such symmetries can be encoded geometrically in a Schrödinger deformation of AdS 3 × S 3 . Finally, in contrast to higher dimensional cases [23,24,25], we note that some curious structure of supercharges is possible in the present case, due to the low-dimensionality. As an example, we identify an algebra with 2 dynamical and 2 conformal supercharges, which is closed, without kinematical ones.…”

“…This superalgebra contains 16 supercharges and the related super Schrödinger algebras are obtained as subalgebras of the superalgebra with the help of projection operators. The basic strategy is the same as in [23,24,25]. The bosonic part is universally given by SL(2, R)×U (1) .…”

“…We recall that null-warped AdS 3 is indistinguishable from three-dimensional Schrödinger geometries with dynamical exponent z = 2. Therefore, as has been done in higher dimensions [22,23,24,25], we start with a classification of the various ways of embedding Schrödinger superalgebras in superconformal algebras in three dimensions. More concretely, we focus on the superalgebra psu(1,1|2) ⊕ psu(1,1|2), corresponding to the superconformal symmetry of the geometry AdS 3 × S 3 .…”

“…In[23,24], super Schrödinger algebras are considered from psu(2, 2|4), osp(8|4) and osp(8 * |4). For generalizations to the z = 2 case and classifications of super Lifshitz algebras, see[25].…”

Schrödinger geometries arising from Yang-Baxter deformations

“…According to the Killing spinor analysis in [32], for values satisfying the condition be interesting to study the relation between classical r-matrices and the classification of super Schrödinger algebras [38]. It would also be nice to study the relation to warped AdS 3 geometries, for example, along the line of [39].…”