Photon self-interaction on deformed spacetime

TL;DR

This paper introduces a new nonlocal four-photon interaction model on deformed spacetime, analyzing its properties through one-loop calculations and demonstrating divergence cancellation and elimination of pathological terms.

Contribution

It develops three models of nonlocal four-photon interactions on deformed spacetime using Seiberg-Witten maps, with detailed one-loop analysis showing divergence cancellation and removal of pathological terms.

Findings

Full IR divergence cancellation in models I and II.

Complete elimination of pathological terms in model III.

Identification of parameter conditions for divergence and pathology removal.

Abstract

A novel nonlocal four-photon interaction on the deformed spacetime is derived and studied in the three selected models (I, II, III). The first two models (I, II) are obtained via two distinct second-order $\theta$-exact Seiberg-Witten maps of the noncommutative U(1) gauge field strength on Moyal space. The third one (III), inspired by the manifestly gauge invariant structures emerging in the first two, due to the model generality has been constructed with a different set of freedom parameters. The physical relevancy of all models is analyzed by evaluating the four-photon-tadpole diagram, which, when combined with the bubble graph, enables us to fully consider all contributions to the one-loop photon polarization tensor. For an arbitrary noncommutative matrix theta^\mu\nu, the full quadratic IR divergence cancellation in the one-loop photon two-point function is obtained with particular combinations of Seiberg-Witten map/gauge-symmetry freedom parameters in models I and II. Finally, our model III enables complete elimination of all pathological terms in the photon polarization tensor at one-loop order if a special value for the theta matrix is chosen.