Noncritical osp(1|2,R) M-theory matrix model with an arbitrary time dependent cosmological constant

Dimensional reduction of the D = 2 minimal super Yang-Mills to the D = 1 matrix quantum mechanics is shown to double the number of dynamical supersymmetries, from N = 1 to N = 2. We analyze the most general supersymmetric deformations of the latter, in order to construct the noncritical 3D M-theory matrix model on generic supersymmetric backgrounds. It amounts to adding quadratic and linear potentials with arbitrary time dependent coefficients, namely, a cosmological ‘constant,’ Λ(t), and an electric flux background, ρ(t), respectively. The resulting matrix model enjoys, irrespective of Λ(t) and ρ(t), two dynamical supersymmetries which further reveal three hidden so(1, 2) symmetries. All together they form the supersymmetry algebra, osp(1|2,R). Each so(1, 2) multiplet in the Hilbert space visualizes a dynamics constrained on either Euclidean or Minkowskian dS2/AdS2 space, depending on its Casimir. In particular, all the unitary multiplets have the Euclidean dS2/AdS2 geometry. We argue that the matrix model provides holographic duals to the 2D superstring theories on various backgrounds having the spacetime signature Minkowskian if Λ(t) > 0, or Euclidean if Λ(t) < 0. In particular, we conjecture that the choice of Λ being negative constant corresponds to the N = 2 super Liouville theory.