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

TL;DR

This paper constructs a supersymmetric matrix model with arbitrary time-dependent cosmological constant and electric flux, revealing hidden symmetries and potential holographic duals to 2D superstring theories on diverse backgrounds.

Contribution

It introduces a novel noncritical 3D M-theory matrix model with arbitrary time-dependent parameters, extending previous models and uncovering hidden osp(1|2,R) supersymmetry and geometric structures.

Findings

The model maintains two dynamical supersymmetries regardless of Lambda(t) and rho(t).

It reveals three hidden so(1,2) symmetries forming osp(1|2,R).

Unitary multiplets correspond to Euclidean dS_{2}/AdS_{2} geometries.

Abstract

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,' Lambda(t), and an electric flux background, rho(t), respectively. The resulting matrix model enjoys, irrespective of Lambda(t) and rho(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 dS_{2}/AdS_{2} space, depending on its Casimir. In particular, all the unitary multiplets have the Euclidean dS_{2}/AdS_{2} geometry. We argue that the matrix model provides holographic duals to the 2D superstring theories on various backgrounds having the spacetime signature Minkowskian if Lambda(t)>0, or Euclidean if Lambda(t)<0.