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  • Letter
  • Open Access

Root-TT¯ flows unify 4D duality-invariant electrodynamics and 2D integrable sigma models

H. Babaei-Aghbolagh1,*, Bin Chen1,2,†, and Song He1,3,‡

  • *Contact author: hosseinbabaei@nbu.edu.cn
  • †Contact author: chenbin1@nbu.edu.cn
  • ‡Contact author: hesong@nbu.edu.cn
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Phys. Rev. D 112, L101702 – Published 21 November, 2025

DOI: https://doi.org/10.1103/1r4p-3r5q

Abstract

We present a single, dimension-independent framework that links four-dimensional duality-invariant nonlinear electrodynamics to two-dimensional integrable sigma models. Both sectors are shown to obey the same firs-order Courant–Hilbert equation, solved by a common generating function and an auxiliary-potential formulation. Within this structure, a discrete φ parity acts as a selection rule, organizing deformation series into integer versus fractional powers. Two commuting deformations—an irrelevant parameter λ and a marginal parameter γ—admit universal flow representations that recover root-TT¯ dynamics and extend them in a controlled way. The construction yields closed-form families (generalized Born-Infeld, logarithmic, and q deformed) and a new integrable model, all realized in 2D and 4D. These results replace case-by-case analyses with a unified route to solvable nonlinear theories, with immediate relevance to gauge dynamics, string-inspired effective actions, and integrable models.

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Phys. Rev. D 112, L101702– Published 21 November, 2025
  • Received 26 August 2025
  • Accepted 24 October 2025
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