Troubles with Spacetime Noncommutative Theories: Tachyons or S-branes?

TL;DR

This paper investigates Lorentzian solutions in spacetime noncommutative gauge theories, revealing issues with the perturbative S matrix due to localized degrees, and identifies special cases where these problems are resolved.

Contribution

It demonstrates the existence of localized Lorentzian solutions and analyzes conditions under which the S matrix formulation remains consistent in noncommutative theories.

Findings

Localized solutions challenge S matrix formulation

Problems vanish when noncommutativity is purely spatial

Lightlike noncommutativity with orthogonal electric and magnetic parts resolves issues

Abstract

We find Lorentzian solutions of spacetime noncommutative gauge theories that are localized exponentially in space and time. Together with time translational invariance of the theories, we argue that perurbative S matrix formulation of such theories is problematic in the sense that the S matrix based on free in and out states misses the spacetime localized degrees. We show that, in 3+1 dimensions, the problem disappears for the cases where the noncommutativity becomes purely spatial by an appropriate Lorentz transformation or the noncommutativity is lightlike with its electric and magnetic parts orthogonal to each other.