The Triple $T\bar{T}$-Like Flow in Quantum Field Theories: Irrelevant, Marginal, and Relevant

Abstract

We introduce a one-parameter root-$T\bar{T}$-like flow, ${\partial }_{\lambda }\mathcal{L}={\mathcal{R}}_{\lambda }^{1/\alpha }$, which organizes stress-tensor deformations into irrelevant, marginal, and relevant branches. Within duality-invariant electrodynamics in four dimensions, and equivalently within two-dimensional integrable sigma models, the flow admits a closed-form solution controlled by an auxiliary equation. The marginal point $\alpha =1$ reproduces the root-$T\bar{T}$ / ModMax branch, while $\alpha <1$ gives irrelevant deformations distinct from the standard Born-Infeld $T\bar{T}$ flow. For $\alpha >1$, the same construction yields explicit relevant $T\bar{T}$-like Lagrangians. These results suggest that root-$T\bar{T}$ flows provide a common organizing principle for duality-invariant and integrable deformations.

7 pages, no figures, comments welcome