The Large N Reduction in Matrix Quantum Mechanics -- a Bridge between BFSS and IKKT --

TL;DR

This paper investigates the large N reduction in matrix quantum mechanics, confirming its validity for both bosonic and supersymmetric cases, and establishes a connection between the BFSS and IKKT models for nonperturbative M-theory studies.

Contribution

It demonstrates the large N reduction's applicability to matrix quantum mechanics and links the BFSS and IKKT models, facilitating cross-model insights.

Findings

Monte Carlo results confirm the equivalence in the bosonic case

Schwinger-Dyson equations offer an explanation for the equivalence

The equivalence likely holds in the supersymmetric case with care for symmetry breaking

Abstract

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 model may be useful in studying supersymmetric and/or chiral gauge theories nonperturbatively. We apply this idea to matrix quantum mechanics, which is relevant, for instance, to nonperturbative studies of the BFSS Matrix Theory, a conjectured nonperturbative definition of M-theory. In the bosonic case we present Monte Carlo results confirming the equivalence directly, and discuss a possible explanation based on the Schwinger-Dyson equations. In the supersymmetric case we argue that the equivalence holds as well although some care should be taken if the rotational symmetry is spontaneously broken. This equivalence provides an explicit relation between the BFSS model and the IKKT model, which may be used to translate results in one model to the other.