# Matrix model and Yukawa couplings on the noncommutative torus

## TL;DR

This paper develops a Dirac operator on the noncommutative torus compatible with the IKKT model, analyzes zero modes with magnetic fluxes, and computes Yukawa couplings for chiral matter, advancing noncommutative geometry in string theory.

## Contribution

It introduces a Dirac operator on the noncommutative torus aligned with the IKKT model and calculates Yukawa couplings for chiral matter fields.

## Key findings

- Zero-mode solutions exhibit chirality and generation structure similar to the commutative case.
- Yukawa couplings for chiral matter fields are explicitly computed.
- The Dirac operator is consistent with the non-perturbative IKKT model.

## Abstract

The IKKT model is proposed as a non-perturbative formulation of superstring theory. We propose a Dirac operator on the noncommutative torus,which is consistent with the IKKT model, based on noncommutative geometry. Next, we consider zero-mode equations of the Dirac operator with magnetic fluxes. We find that zero-mode solutions have the chirality and the generation structures similar to the commutative case. Moreover, we compute Yukawa couplings of chiral matter fields.