Complex Langevin studies of the dynamical compactification of extra dimensions in the Euclidean IKKT matrix model

TL;DR

This study uses the Complex Langevin Method to investigate spontaneous symmetry breaking in the Euclidean IKKT matrix model, providing evidence that SO(10) symmetry breaks to SO(3), aligning with previous Gaussian Expansion Method results.

Contribution

It applies the Complex Langevin Method to the Euclidean IKKT matrix model to analyze symmetry breaking, offering new computational insights into the model's nonperturbative behavior.

Findings

SO(10) symmetry breaks to SO(3)

Results agree with Gaussian Expansion Method

Supports the model as a nonperturbative superstring formulation

Abstract

The type IIB matrix model, also known as the IKKT matrix model, is a promising candidate for a nonperturbative formulation of superstring theory. In this talk we study the Euclidean version of the IKKT matrix model, which has a "sign problem" due to the Pfaffian coming from integrating out the fermionic degrees of freedom. To study the spontaneous breaking of the SO(10) rotational symmetry, we apply the Complex Langevin Method (CLM) to the Euclidean IKKT matrix model. We conclude that the SO(10) symmetry is broken to SO(3), in agreement with the previous studies by the Gaussian Expansion Method (GEM). We also apply the GEM to the deformed model and find consistency with the CLM result. These are proceedings of Takehiro Azuma's talk at Asia-Pacific Symposium for Lattice Field Theory (APLAT 2020) on August 4-7, 2020, based on the paper arXiv:2002.07410.