One-loop Photon's Effective Action in the Noncommutative Scalar QED${}_3$

Abstract

In this paper, we consider the evaluation of the effective action for photons coupled to charged scalar fields in the framework of a $(2+1)$-dimensional noncommutative spacetime. In order to determine the noncommutative Maxwell Lagrangian density, we follow a perturbative approach, by integrating out the charged scalar fields, to compute the respective graphs for the vev's $⟨AA⟩$, $⟨AAA⟩$ and $⟨AAAA⟩$. Surprisingly, it is shown that these contributions are planar and that, in the highly noncommutative limit, correspond to the Maxwell effective action and its higher-derivative corrections. It is explicitly verified that the one-loop effective action is gauge invariant, as well as under discrete symmetries: parity, time reversal and charge conjugation. Moreover, a comparison of the main results with the noncommutative QED${}_3$ is established. In particular, the main difference is the absence of parity violating terms in the photon's effective action coming from integrating out the charged scalar fields.

arXiv comment18 pages, 3 figures, published version

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