Causal self-dual nonlinear electrodynamics from the Born-Infeld theory
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| Format: | Preprint |
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2026
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| author | Kuzenko, Sergei M. Ruhl, Jonah |
| author_facet | Kuzenko, Sergei M. Ruhl, Jonah |
| contents | Recently we have proposed a new auxiliary-field formulation for self-dual nonlinear electrodynamics (NLED) which makes use of two building blocks: (i) a seed self-dual theory $L(F_{μν};g)$, where $F_{μν}$ is the electromagnetic field strength and $g$ a duality-invariant coupling constant; and (ii) a scalar potential $W(ψ)$. Our formulation is based on the Lagrangian $ \mathfrak{L}(F_{μν};ψ) = L(F_{μν};ψ) + W(ψ)$, where $ψ$ is an auxiliary scalar field. Integrating out $ψ$, using its equation of motion, one obtains a $\mathsf{U}(1)$ duality-invariant NLED. Different self-dual NLEDs are derived by choosing different potentials $W(ψ)$. In the case that the seed Lagrangian defines the Born-Infeld theory, in this paper we demonstrate that the resulting models for self-dual NLED are causal and provide a general solution of the self-duality equation. We also elaborate on the procedure to relate our formulation to that developed by Russo and Townsend. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_06193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Causal self-dual nonlinear electrodynamics from the Born-Infeld theory Kuzenko, Sergei M. Ruhl, Jonah High Energy Physics - Theory Mathematical Physics Recently we have proposed a new auxiliary-field formulation for self-dual nonlinear electrodynamics (NLED) which makes use of two building blocks: (i) a seed self-dual theory $L(F_{μν};g)$, where $F_{μν}$ is the electromagnetic field strength and $g$ a duality-invariant coupling constant; and (ii) a scalar potential $W(ψ)$. Our formulation is based on the Lagrangian $ \mathfrak{L}(F_{μν};ψ) = L(F_{μν};ψ) + W(ψ)$, where $ψ$ is an auxiliary scalar field. Integrating out $ψ$, using its equation of motion, one obtains a $\mathsf{U}(1)$ duality-invariant NLED. Different self-dual NLEDs are derived by choosing different potentials $W(ψ)$. In the case that the seed Lagrangian defines the Born-Infeld theory, in this paper we demonstrate that the resulting models for self-dual NLED are causal and provide a general solution of the self-duality equation. We also elaborate on the procedure to relate our formulation to that developed by Russo and Townsend. |
| title | Causal self-dual nonlinear electrodynamics from the Born-Infeld theory |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2605.06193 |