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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.14583 |
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| _version_ | 1866915482149322752 |
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| author | Babaei-Aghbolagh, H. He, Song Ouyang, Hao |
| author_facet | Babaei-Aghbolagh, H. He, Song Ouyang, Hao |
| contents | We demonstrate that the necessary condition for $SO(N) \times SO(N)$ duality invariance manifests as a partial differential equation in two-dimensional scalar theories. This condition, expressed as a partial differential equation, corresponds precisely to the integrability condition. We derive a general perturbation solution to this partial differential equation, which includes both a root $T\bar{T}$ flow equation and an irrelevant $T\bar{T}$-like flow equation. Additionally, we identify a general form for these flow equations that commute with each other. Our results establish a general integrable theory characterized by theory-dependent coefficients at each order in the $λ$-expansion. This unified framework systematically classifies all integrable theories possessing two Lorentz-invariant variables ($P_1$, $P_2$) while accommodating arbitrary orders of the coupling constants ($λ$, $γ$). The theory provides a comprehensive classification scheme that encompasses both known and novel integrable systems within this class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized $T\bar{T}$-like flows for scalar theories in two dimensions Babaei-Aghbolagh, H. He, Song Ouyang, Hao High Energy Physics - Theory We demonstrate that the necessary condition for $SO(N) \times SO(N)$ duality invariance manifests as a partial differential equation in two-dimensional scalar theories. This condition, expressed as a partial differential equation, corresponds precisely to the integrability condition. We derive a general perturbation solution to this partial differential equation, which includes both a root $T\bar{T}$ flow equation and an irrelevant $T\bar{T}$-like flow equation. Additionally, we identify a general form for these flow equations that commute with each other. Our results establish a general integrable theory characterized by theory-dependent coefficients at each order in the $λ$-expansion. This unified framework systematically classifies all integrable theories possessing two Lorentz-invariant variables ($P_1$, $P_2$) while accommodating arbitrary orders of the coupling constants ($λ$, $γ$). The theory provides a comprehensive classification scheme that encompasses both known and novel integrable systems within this class. |
| title | Generalized $T\bar{T}$-like flows for scalar theories in two dimensions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2501.14583 |