Some Aspects on Non-commutative Theories with a compactified Extra-Dimension

TL;DR

This paper explores the effects of an extra compactified dimension in non-commutative space-time, analyzing how the compactification radius and non-commutative parameter influence physical scenarios, including Minkowski space recovery and gravitational potential modifications.

Contribution

It introduces two models linking the compactification radius and non-commutative parameter, providing insights into their impact on space-time structure and gravitational interactions.

Findings

Relation between compactification radius and non-commutative parameter established

Recovery of Minkowski space in certain limits demonstrated

Modified gravitational potential for cosmic strings analyzed

Abstract

We study some aspects when one consider the existence of one extra-dimension in addition to a non-commutative space-time. We present here two different examples, where the first one provides a scenario were it is possible to relate the variations on the compactification radius $L$ and the non-commutative parameter $\theta^{\mu\nu}$, recovering the usual Minkowski $(3+1)D$ metric and, in the other one, we can set a simple relationship between this radius and $\theta$, the non-commutative parameter, for the gravitational potential between a point particle and a straight cosmic string in $(2+1)D$.