The large-N reduction in matrix quantum mechanics - a bridge between BFSS and IKKT

The large-N reduction is an equivalence between large-N gauge theories and matrix models discovered by Eguchi and Kawai in the early 80s. In particular the continuum version of the quenched Eguchi-Kawai (cQEK) model may be useful in studying supersymmetric and/or chiral gauge theories nonperturbatively. Unlike the original lattice version, however, the equivalence for the cQEK model is highly nontrivial. We study this model in the case of matrix quantum mechanics, i.e., the large-N gauge theory in one dimension. In the bosonic case we provide a direct confirmation of the equivalence by Monte Carlo simulations, and discuss an explanation based on the Schwinger-Dyson equations. In the supersymmetric case we argue that the equivalence holds as well possibly with some care when one takes the large-N limit. This equivalence provides an explicit relation between the BFSS model and the IKKT model, which are conjectured nonperturbative formulations of M-theory and type IIB superstring theory, respectively. In particular we conjecture that the SO(9) symmetry of the BFSS model is spontaneously broken if an analogous phenomenon occurs in the IKKT model as suggested by recent works