Integrable Sigma Models and Universal Root $T\bar{T}$ Deformation via Courant-Hilbert Approach
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Babaei-Aghbolagh, H. Chen, Bin He, Song |
| author_facet | Babaei-Aghbolagh, H. Chen, Bin He, Song |
| contents | We develop a unified Courant--Hilbert framework for constructing two-dimensional integrable sigma models deformed by two couplings: a marginal one $γ$ and an irrelevant one $λ$. The integrability condition is encoded in a nonlinear partial differential equation (PDE) for two invariants $(P_1, P_2)$, whose general solution could be expressed through an arbitrary generating function $\ell(τ)$. This formulation encompasses and extends known models, such as ModMax and Born-Infeld, while introducing new classes of solvable models with closed-form Lagrangians, including those with logarithmic and $q$-deformations. All resulting theories obey a universal root-$T\overline{T}$ flow equation, consistent under dimensional reduction from four-dimensional duality-invariant electrodynamics. Using perturbative expansions, we recover ModMax in the free limit, determine the $γ$-dependence of the coupling functions, and show how different flow equations, including a single-trace form, naturally emerge. Our results reveal deep structural connections between self-duality, integrability, and deformation dynamics across different dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17075 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrable Sigma Models and Universal Root $T\bar{T}$ Deformation via Courant-Hilbert Approach Babaei-Aghbolagh, H. Chen, Bin He, Song High Energy Physics - Theory We develop a unified Courant--Hilbert framework for constructing two-dimensional integrable sigma models deformed by two couplings: a marginal one $γ$ and an irrelevant one $λ$. The integrability condition is encoded in a nonlinear partial differential equation (PDE) for two invariants $(P_1, P_2)$, whose general solution could be expressed through an arbitrary generating function $\ell(τ)$. This formulation encompasses and extends known models, such as ModMax and Born-Infeld, while introducing new classes of solvable models with closed-form Lagrangians, including those with logarithmic and $q$-deformations. All resulting theories obey a universal root-$T\overline{T}$ flow equation, consistent under dimensional reduction from four-dimensional duality-invariant electrodynamics. Using perturbative expansions, we recover ModMax in the free limit, determine the $γ$-dependence of the coupling functions, and show how different flow equations, including a single-trace form, naturally emerge. Our results reveal deep structural connections between self-duality, integrability, and deformation dynamics across different dimensions. |
| title | Integrable Sigma Models and Universal Root $T\bar{T}$ Deformation via Courant-Hilbert Approach |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.17075 |