Non-local Field Theories and the Non-commutative Torus

TL;DR

This paper explores how taking specific limits of super Yang-Mills theories on non-commutative tori can lead to non-local field theories on non-compact spaces, with potential implications for higher-dimensional theories.

Contribution

It introduces a method to derive non-local field theories from non-commutative geometries, extending to (2,0) theories and their DLCQ formulations.

Findings

A limit of SYM on non-commutative torus yields a non-local theory on non-compact space.

The approach generalizes to (2,0) theories in 5+1 dimensions.

The DLCQ of the generalized theory is known.

Abstract

We argue that by taking a limit of SYM on a non-commutative torus one can obtain a theory on non-compact space with a finite non-locality scale. We also suggest that one can also obtain a similar generalization of the (2,0) field theory in 5+1 dimensions, and that the DLCQ of this theory is known.