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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2409.05165 |
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| _version_ | 1866909308711600128 |
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| author | Li, Jian-Rong Su, Changjian Yang, Qinglin |
| author_facet | Li, Jian-Rong Su, Changjian Yang, Qinglin |
| contents | In quantum field theory study, Grassmannian manifolds $\text{Gr}(4,n)$ are closely related to $D{=}4$ kinematics input for $n$-particle scattering processes, whose combinatorial and geometrical structures have been widely applied in studying conformal invariant physical theories and their scattering amplitudes. Recently, \cite{HLY21} observed that constraining $D{=}4$ kinematics input to its $D{=}3$ subspace can be interpreted as folding Grassmannian cluster algebras $\mathbb{C}[\text{Gr}(4,n)]$. In this paper, we deduce general expressions for these constraints in terms of Plücker variables of $\text{Gr}(4,n)$ directly from $D{=}3$ subspace definition, and propose a series of initial quivers for algebra $\mathbb{C}[\text{Gr}(4,n)]$ whose folding conditions exactly meet the constraints, which proves the observation finally. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dual conformal invariant kinematics and folding of Grassmannian cluster algebras Li, Jian-Rong Su, Changjian Yang, Qinglin Mathematical Physics High Energy Physics - Theory In quantum field theory study, Grassmannian manifolds $\text{Gr}(4,n)$ are closely related to $D{=}4$ kinematics input for $n$-particle scattering processes, whose combinatorial and geometrical structures have been widely applied in studying conformal invariant physical theories and their scattering amplitudes. Recently, \cite{HLY21} observed that constraining $D{=}4$ kinematics input to its $D{=}3$ subspace can be interpreted as folding Grassmannian cluster algebras $\mathbb{C}[\text{Gr}(4,n)]$. In this paper, we deduce general expressions for these constraints in terms of Plücker variables of $\text{Gr}(4,n)$ directly from $D{=}3$ subspace definition, and propose a series of initial quivers for algebra $\mathbb{C}[\text{Gr}(4,n)]$ whose folding conditions exactly meet the constraints, which proves the observation finally. |
| title | Dual conformal invariant kinematics and folding of Grassmannian cluster algebras |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.05165 |