Abstract
We study the Heisenberg-Euler effective action in constant electromagnetic fields \( \overline{F} \) for QED with N charged particle flavors of the same mass and charge e in the large N limit characterized by sending N → ∞ while keeping Ne2 ∼ \( e\overline{F} \) ∼ N0 fixed. This immediately implies that contributions that scale with inverse powers of N can be neglected and the resulting effective action scales linearly with N . Interestingly, due to the presence of one-particle reducible diagrams, even in this limit the Heisenberg-Euler effective action receives contributions of arbitrary loop order. In particular for the special cases of electric- and magnetic-like field configurations we construct an explicit expression for the associated effective Lagrangian that, upon extremization for two constant scalar coefficients, allows to evaluate its full, all-order result at arbitrarily large field strengths. We demonstrate that our manifestly nonperturbative expression correctly reproduces the known results for the Heisenberg-Euler effective action at large N , namely its all-loop strong field limit and its low-order perturbative expansion in powers of the fine-structure constant.
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Acknowledgments
This work has been funded by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. 416607684 within the Research Unit FOR2783/2. I would like to thank Gerald V. Dunne for comments and inspiring discussions.
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Karbstein, F. Towards the full Heisenberg-Euler effective action at large N. J. High Energ. Phys. 2024, 180 (2024). https://doi.org/10.1007/JHEP02(2024)180
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DOI: https://doi.org/10.1007/JHEP02(2024)180