Soliton Surfaces and the Geometry of Integrable Deformations of the $\mathbb{CP}^{N-1}$ Model
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| Format: | Preprint |
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2025
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| author | Ferko, Christian Galli, Michele Huang, Zejun Tartaglino-Mazzucchelli, Gabriele |
| author_facet | Ferko, Christian Galli, Michele Huang, Zejun Tartaglino-Mazzucchelli, Gabriele |
| contents | The $\mathbb{CP}^{N-1}$ model is an analytically tractable $2d$ quantum field theory which shares several properties with $4d$ Yang-Mills theory. By virtue of its classical integrability, this model also admits a family of integrable higher-spin auxiliary field deformations, including the $T \overline{T}$ deformation as a special case. We study the $\mathbb{CP}^{N-1}$ model and its deformations from a geometrical perspective, constructing their soliton surfaces and recasting physical properties of these theories as statements about surface geometry. We examine how the $T \overline{T}$ flow affects the unit constraint in the $\mathbb{CP}^{N-1}$ model and prove that any solution of this theory with vanishing energy-momentum tensor remains a solution under analytic stress tensor deformations -- an argument that extends to generic dimensions and instanton-like solutions in stress tensor flows including the non-analytic, $2d$, root-$T \overline{T}$ case and classes of higher-spin, Smirnov-Zamolodchikov-type, deformations. Finally, we give two geometric interpretations for general $T \overline{T}$-like deformations of symmetric space sigma models, showing that such flows can be viewed as coupling the undeformed theory to a unit-determinant field-dependent metric, or using a particular choice of moving frame on the soliton surface. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soliton Surfaces and the Geometry of Integrable Deformations of the $\mathbb{CP}^{N-1}$ Model Ferko, Christian Galli, Michele Huang, Zejun Tartaglino-Mazzucchelli, Gabriele High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems The $\mathbb{CP}^{N-1}$ model is an analytically tractable $2d$ quantum field theory which shares several properties with $4d$ Yang-Mills theory. By virtue of its classical integrability, this model also admits a family of integrable higher-spin auxiliary field deformations, including the $T \overline{T}$ deformation as a special case. We study the $\mathbb{CP}^{N-1}$ model and its deformations from a geometrical perspective, constructing their soliton surfaces and recasting physical properties of these theories as statements about surface geometry. We examine how the $T \overline{T}$ flow affects the unit constraint in the $\mathbb{CP}^{N-1}$ model and prove that any solution of this theory with vanishing energy-momentum tensor remains a solution under analytic stress tensor deformations -- an argument that extends to generic dimensions and instanton-like solutions in stress tensor flows including the non-analytic, $2d$, root-$T \overline{T}$ case and classes of higher-spin, Smirnov-Zamolodchikov-type, deformations. Finally, we give two geometric interpretations for general $T \overline{T}$-like deformations of symmetric space sigma models, showing that such flows can be viewed as coupling the undeformed theory to a unit-determinant field-dependent metric, or using a particular choice of moving frame on the soliton surface. |
| title | Soliton Surfaces and the Geometry of Integrable Deformations of the $\mathbb{CP}^{N-1}$ Model |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2509.05081 |