Towards the full Heisenberg-Euler effective action at large $N$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914689499267072 |
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| author | Karbstein, Felix |
| author_facet | Karbstein, Felix |
| contents | We study the Heisenberg-Euler effective action in constant electromagnetic fields $\bar{F}$ for QED with $N$ charged particle flavors of the same mass and charge $e$ in the large $N$ limit characterized by sending $N\to\infty$ while keeping $Ne^2\sim e\bar{F}\sim N^0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09804 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards the full Heisenberg-Euler effective action at large $N$ Karbstein, Felix High Energy Physics - Theory High Energy Physics - Phenomenology We study the Heisenberg-Euler effective action in constant electromagnetic fields $\bar{F}$ for QED with $N$ charged particle flavors of the same mass and charge $e$ in the large $N$ limit characterized by sending $N\to\infty$ while keeping $Ne^2\sim e\bar{F}\sim N^0$ 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. |
| title | Towards the full Heisenberg-Euler effective action at large $N$ |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2312.09804 |