Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking

TL;DR

This paper investigates how extra dimensions in the Euclidean IKKT matrix model dynamically compactify through spontaneous symmetry breaking, using numerical simulations with complex Langevin method and Gaussian expansion method.

Contribution

It provides evidence of dynamical compactification of extra dimensions in the Euclidean IKKT matrix model via SSB, employing novel numerical techniques to overcome complex action challenges.

Findings

Evidence of SO(3) symmetric vacuum in the model

Confirmation of SSB pattern consistent with previous methods

Successful application of complex Langevin and Gaussian expansion methods

Abstract

The IKKT matrix model has been conjectured to provide a promising nonperturbative formulation of superstring theory. In this model, spacetime emerges dynamically from the microscopic matrix degrees of freedom in the large-N limit, and Monte Carlo simulations of the Lorentzian version provide evidence of an emergent (3+1)-dimensional expanding space-time. In this talk, we discuss the Euclidean version of the IKKT matrix model and provide evidence of dynamical compactification of the extra dimensions via the spontaneous symmetry breaking (SSB) of the 10D rotational symmetry. We perform numerical simulations of a system with a severe complex action problem by using the complex Langevin method (CLM). The CLM suffers from the singular-drift problem and we deform the model in order to avoid it. We study the SSB pattern as we vary the deformation parameter and we conclude that the original model has an SO(3) symmetric vacuum, in agreement with previous calculations using the Gaussian expansion method (GEM). We employ the GEM to the deformed model and we obtain results consistent with the ones obtained by CLM.