通过φ奇偶性和无关变形分类自偶非线性电动力学
Classifying Causal Nonlinear Electrodynamics via $φ$-Parity and Irrelevant Deformations
AI总结：
本文通过分析自偶非线性电动力学理论的解析性性质，利用φ奇偶性不变性，分类了由能量动量张量标量的整数次幂构建的无关变形理论，以及涉及整数和半整数次幂的非解析理论。
摘要：
我们研究了基于其解析性性质的自偶非线性电动力学（NED）理论的分类，这些性质直接与离散φ奇偶性变换的不变性相关。这种分类通过生成理论的无关T\bar{T}-样变形的结构来表达，这些变形从马克斯韦种子生成理论。使用闭式和微扰方法在库兰-希尔（CH）和鲁索-汤森德辅助场形式化中，我们展示了精确的对应关系：φ奇偶性不变、解析理论由由能量动量张量标量的整数次幂构建的无关变形生成，即\mathcal{O}_\lambda\sim \sum C_m (T_{\mu\nu}T^{\mu\nu})^{1-m}({T_\mu}^\mu{T_\nu}^\nu)^{m}。相反，φ奇偶性破坏、非解析理论需要涉及整数和半整数次幂的变形，即\mathcal{O}_\lambda\sim \sum C_m (T_{\mu\nu}T^{\mu\nu})^{1-m/2}({T_\mu}^\mu{T_\nu}^\nu)^{m/2}。我们通过微扰CH框架证明了这一结果，显示φ奇偶性不变性对CH函数\ell(\tau)的展开系数施加了特定约束，从而迫使所有半整数次幂在变形中消失。该分类在已知的闭式理论中得到明确验证：解析广义Born-Infeld模型和非解析的q=3/4变形以及“无τ最大值”理论的例子。此外，我们还展示了在存在边缘根-T\bar{T}耦合γ的情况下，φ奇偶性变换如何一致地推广，并推导了所研究理论的相应边缘和无关流方程。
英文摘要：
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.
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