Exact $T\bar{T}$-Like Flows in Nonlinear Electrodynamics

We derive an exact nonperturbative $T\bar{T}$-like flow for the class of one-scale, self-dual nonlinear electrodynamics theories admitting a Courant–Hilbert representation. The flow has a universal parametric form in terms of the defining Courant–Hilbert function and, on any physical branch where the relevant invariant map is invertible, becomes an autonomous function of the two quadratic stress-tensor invariants, ${\mathrm{\partial }}_{\lambda }\mathcal{L}=X\mathcal{F}(Y\mathrm{/}X)$. The function $\mathcal{F}$ is model dependent, and global autonomy is assumed when the invariant map is one-to-one. Born–Infeld theory yields a quadratic stress-tensor flow, whereas the causal Russo–Townsend logarithmic model gives an exact nonlinear expression involving the Lambert $W$ function whose weak-field expansion reproduces the known perturbative result. We also establish the equivalence with the Russo–Townsend auxiliary-field formulation. These results provide an exact construction of autonomous irrelevant flows for a broad, explicitly specified class of self-dual nonlinear electrodynamics theories.