Title: Root-$T\bar{T}$ Deformations On Causal Self-Dual Electrodynamics Theories Show Chinese title

Title: 根$T\bar{T}$变形 在因果自对偶电动力学理论中

Abstract: The self-dual condition, which ensures invariance under electromagnetic duality, manifests as a partial differential equation in nonlinear electromagnetism theories. The general solution to this equation is expressed in terms of an auxiliary field, $\tau$, and Courant-Hilbert functions, $\ell(\tau)$, which depend on $\tau$. Recent studies have shown that duality-invariant nonlinear electromagnetic theories fulfill the principle of causality under the conditions $\frac{\partial \ell}{\partial \tau} \ge 1$ and $\frac{\partial^2 \ell}{\partial \tau^2} \ge 0$. In this paper, we investigate theories with two coupling constants that also comply with the principle of causality. We demonstrate that these theories possess a new universal representation of the root-$T\bar{T}$ operator. Additionally, we derive marginal and irrelevant flow equations for the logarithmic causal self-dual electrodynamics and identify a symmetry referred to as $\alpha$-symmetry, which is present in all these models. Show Chinese abstract

Abstract: 自对偶条件确保在电磁对偶性下的不变性，在非线性电磁理论中表现为一个偏微分方程。 该方程的一般解用辅助场$\tau$和依赖于$\tau$的 Courant-Hilbert 函数$\ell(\tau)$表示。 最近的研究表明，在条件$\frac{\partial \ell}{\partial \tau} \ge 1$和$\frac{\partial^2 \ell}{\partial \tau^2} \ge 0$下，满足对偶性的非线性电磁理论符合因果性原理。 在本文中，我们研究了也符合因果性原理的两个耦合常数的理论。 我们证明这些理论具有根$T\bar{T}$算子的新普遍表示。 此外，我们推导了对数因果自对偶电动力学的边缘和无关流方程，并确定了一种称为$\alpha$-对称性的对称性，这种对称性存在于所有这些模型中。