Classifying Causal Nonlinear Electrodynamics via $φ$-Parity and Irrelevant Deformations
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2026
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| author | Babaei-Aghbolagh, H. Velni, Komeil Babaei He, Song Pezhman, Zahra |
| author_facet | Babaei-Aghbolagh, H. Velni, Komeil Babaei He, Song Pezhman, Zahra |
| contents | We investigate the classification of self-dual nonlinear electrodynamic (NED) theories based on their analyticity properties, which are directly linked to invariance under a discrete $φ$-parity transformation. This classification is expressed through the structure of the irrelevant $T\bar{T}$-like deformations that generate the theories from a Maxwell seed. Using both closed-form and perturbative methods within the Courant-Hilbert (CH) and Russo-Townsend auxiliary field formalisms, we demonstrate a precise correspondence: $φ$-parity-invariant, analytic theories are generated by irrelevant deformations built from integer powers of the energy-momentum tensor scalars, $\mathcal{O}_λ\sim \sum C_m (T_{μν}T^{μν})^{1-m}({T_μ}^μ{T_ν}^ν)^{m}$. Conversely, $φ$-parity-violating, non-analytic theories require deformations involving both integer and half-integer powers, $\mathcal{O}_λ\sim \sum C_m (T_{μν}T^{μν})^{1-m/2}({T_μ}^μ{T_ν}^ν)^{m/2}$. We prove this result in generality via a perturbative CH framework, showing that $φ$-parity invariance imposes specific constraints on the expansion coefficients of the CH function $\ell(τ)$ which, in turn, force all half-integer powers in the deformation to vanish. The classification is explicitly verified for known closed-form theories: the analytic generalized Born-Infeld model and the non-analytic examples of the $q=3/4$-deformed and "no $τ$-maximum" theories. Furthermore, we show how the $φ$-parity transformation is consistently generalized in the presence of a marginal root-$T\bar{T}$ coupling $γ$, and we derive the corresponding marginal and irrelevant flow equations for the studied theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_03426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classifying Causal Nonlinear Electrodynamics via $φ$-Parity and Irrelevant Deformations Babaei-Aghbolagh, H. Velni, Komeil Babaei He, Song Pezhman, Zahra High Energy Physics - Theory We investigate the classification of self-dual nonlinear electrodynamic (NED) theories based on their analyticity properties, which are directly linked to invariance under a discrete $φ$-parity transformation. This classification is expressed through the structure of the irrelevant $T\bar{T}$-like deformations that generate the theories from a Maxwell seed. Using both closed-form and perturbative methods within the Courant-Hilbert (CH) and Russo-Townsend auxiliary field formalisms, we demonstrate a precise correspondence: $φ$-parity-invariant, analytic theories are generated by irrelevant deformations built from integer powers of the energy-momentum tensor scalars, $\mathcal{O}_λ\sim \sum C_m (T_{μν}T^{μν})^{1-m}({T_μ}^μ{T_ν}^ν)^{m}$. Conversely, $φ$-parity-violating, non-analytic theories require deformations involving both integer and half-integer powers, $\mathcal{O}_λ\sim \sum C_m (T_{μν}T^{μν})^{1-m/2}({T_μ}^μ{T_ν}^ν)^{m/2}$. We prove this result in generality via a perturbative CH framework, showing that $φ$-parity invariance imposes specific constraints on the expansion coefficients of the CH function $\ell(τ)$ which, in turn, force all half-integer powers in the deformation to vanish. The classification is explicitly verified for known closed-form theories: the analytic generalized Born-Infeld model and the non-analytic examples of the $q=3/4$-deformed and "no $τ$-maximum" theories. Furthermore, we show how the $φ$-parity transformation is consistently generalized in the presence of a marginal root-$T\bar{T}$ coupling $γ$, and we derive the corresponding marginal and irrelevant flow equations for the studied theories. |
| title | Classifying Causal Nonlinear Electrodynamics via $φ$-Parity and Irrelevant Deformations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.03426 |