Lattice Superstring and Noncommutative Geometry

TL;DR

This paper explores the connections between superstring theory, noncommutative geometry, and large N gauge theories, highlighting results on the emergence of 4D space-time and properties of noncommutative field theories.

Contribution

It presents new findings on the dynamical generation of 4D space-time in superstring matrix models and discusses noncommutative field theory properties revealed by Monte Carlo simulations.

Findings

Eigenvalue distribution collapse suggests 4D space-time emergence

Monte Carlo simulations reveal dynamical properties of noncommutative field theories

Discussion on lattice construction of supersymmetric gauge theories

Abstract

Recent developments in superstring theory and noncommutative geometry are deeply related to the idea of Eguchi-Kawai reduction in large N gauge theories which dates back to early 80s. After a general review on this subject including revived interests in solving planar QCD, we present some results in the superstring matrix model suggesting the dynamical generation of 4d space-time due to the collapse of the eigenvalue distribution. We then discuss interesting dynamical properties of field theories in noncommutative geometry, which have been revealed by Monte Carlo simulations of twisted reduced models. We conclude with a comment on the recent proposal for a lattice construction of supersymmetric gauge theories based on reduced models.