Supersymmetric extensions of Schrodinger-invariance

Abstract The set of dynamic symmetries of the scalar free Schrodinger equation in d space dimensions gives a realization of the Schrodinger algebra that may be extended into a representation of the conformal algebra in d + 2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin- 1 2 Levy-Leblond equation. An N = 2 supersymmetric extension of these equations leads, respectively, to a ‘super-Schrodinger’ model and to the ( 3 | 2 ) -supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp ( 2 | 2 ) ⋉ sh ( 2 | 2 ) and osp ( 2 | 4 ) , respectively. The Schrodinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrodinger–Neveu–Schwarz algebra sns ( N ) with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp ( 2 | 4 ) . If one includes both N = 2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.