A regularization of field theory on non-commutative torus

TL;DR

This paper introduces a new matrix regularization method for field theory on non-commutative torus, ensuring the product of matrices matches the field product in the large-N limit, addressing previous inconsistencies.

Contribution

A novel regularization procedure using projections in the representation space that aligns matrix products with field products on non-commutative torus.

Findings

The new regularization method resolves product discrepancies.

Matrix products converge to field products in the large-N limit.

Improves consistency of matrix models for non-commutative field theories.

Abstract

Matrix model is used as a regularization of field theory on non-commutative torus. However, there exists an example that the product of the large-N limit of matrices does not coincide with that of the corresponding fields. We propose a new procedure for regularizing fields on a non-commutative torus by matrices with the help of the projection in the representation space, so that the products of the matrices coincide with those of the corresponding fields in the large-N limit.