Non-Commutative Gauge Theories and the Cosmological Constant

TL;DR

This paper explores how non-commutative gauge theories influence the cosmological constant, proposing that non-commutativity acts as a UV cutoff and controls vacuum energy through quantum corrections, supported by two-loop calculations and string theory insights.

Contribution

It introduces the idea that non-commutativity regulates vacuum energy in gauge theories, providing explicit two-loop calculations and string theory arguments for all-order control.

Findings

Vacuum energy scales as 1/θ^2 with non-commutativity parameter θ

Two-loop calculations support the proposed vacuum energy dependence

String theory expressions suggest all-order perturbative control

Abstract

We discuss the issue of the cosmological constant in non-commutative non-supersymmetric gauge theories. In particular, in orbifold field theories non-commutativity acts as a UV cut-off. We suggest that in these theories quantum corrections give rise to a vacuum energy \rho, that is controlled by the non-commutativity parameter \theta, \rho ~ 1/theta^2 (only a soft logarithmic dependence on the Planck scale survives). We demonstrate our claim in a two-loop computation in field theory and by certain higher loop examples. Based on general expressions from string theory, we suggest that the vacuum energy is controlled by non-commutativity to all orders in perturbation theory.