Complex Langevin study of spontaneous symmetry breaking in IKKT matrix model

TL;DR

This study uses complex Langevin dynamics to investigate spontaneous SO(10) symmetry breaking in the Euclidean IKKT matrix model, providing evidence that the phase of the Pfaffian induces symmetry breaking.

Contribution

First application of complex Langevin dynamics to the IKKT matrix model to explore spontaneous symmetry breaking with supersymmetry-preserving deformations.

Findings

Phase of the Pfaffian induces SO(10) symmetry breaking.

Supersymmetry-preserving deformations help evade singular-drift problems.

Evidence supports spontaneous symmetry breaking in the model.

Abstract

The IKKT matrix model, in the large-$N$ limit, is conjectured to be a non-perturbative definition of the ten-dimensional type IIB superstring theory. In this work, we investigate the possibility of spontaneous breaking of the ten-dimensional rotational symmetry in the Euclidean IKKT model. Since the effective action, after integrating out the fermions, is inherently complex, we use the complex Langevin dynamics to study the model. In order to evade the singular-drift problem in the model, we add supersymmetry preserving deformations and then take the vanishing limit of the deformations. Our analysis suggests that the phase of the Pfaffian indeed induces the spontaneous SO(10) symmetry breaking in the Euclidean IKKT model.