Can a Nonsymmetric Metric mimic NCQFT in $e^+e^- \to \gamma \gamma$ ?

Abstract

In the nonsymmetric gravitational theory (NGT) the space-time metric $g_{\mu\nu}$ departs from the flat-space Minkowski form $\eta_{\mu\nu}$ such that it is no longer symmetric, $i.e.$ $g_{\mu\nu} \ne g_{\nu\mu}$. We find that in the most conservative such scenario coupled to quantum field theory, which we call Minimally Nonsymmetric Quantum Field Theory (MNQFT), there are experimentally measurable consequences similar to those from noncommutative quantum field theory (NCQFT). This can be expected from the Seiberg-Witten map which has recently been interpreted as equating gauge theories on noncommutative spacetimes with those in a field dependent gravitational background. In particular, in scattering processes such as the pair annihilation $e^+e^- \to \gamma\gamma$, both theories make the same striking prediction that the azimuthal cross section oscillates in $\phi$. However the predicted number of oscillations differs in the two theories: MNQFT predicts between one and four, whereas NCQFT has no such restriction.