Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations

TL;DR

The paper investigates how non-linear electrodynamics theories—specifically Maxwell, ModMax, Born-Infeld, and generalized Born-Infeld—can be connected through solvable $T\bar{T}$-like deformations. It demonstrates that ModMax deforms under ${O}_{T^2}^{\lambda}$ to yield the generalized Born-Infeld action, linking conformal/duality-invariant NED to BI-type theories; it further introduces a second operator ${O}_{T^2}^{\gamma}$ whose flow preserves duality and contracts Maxwell/ModMax sectors to reproduce ModMax from Maxwell. The work provides exact and perturbative mappings between these theories, clarifying how duality-invariant structures emerge from solvable deformations and offering a framework for potential quantization and higher-dimensional generalizations. Overall, it advances a two-operator, two-parameter picture for generating and organizing non-linear electrodynamics via controlled $T\bar{T}$-like flows.

Abstract

In this letter, we investigate the deformation of the ModMax theory, as a unique Lagrangian of non-linear electrodynamics preserving both conformal and electromagnetic-duality invariance, under $T\bar{T}$-like flows. We will show that the deformed theory is the generalized non-linear Born-Infeld electrodynamics. Being inspired by the invariance under the flow equation for Born-Infeld theories, we propose another $T\bar{T}$-like operator generating the ModMax and generalized Born-Infeld non-linear electrodynamic theories from the usual Maxwell and Born-Infeld theories, respectively.

Figures (1)

• Figure 1: Sequence deformations of the Maxwell theory under ${O}_{T^2}^{\lambda}$ and $O_{T^2}^{\gamma}$.