Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2603.19871 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915877545312256 |
|---|---|
| author | Udagawa, Tadashi |
| author_facet | Udagawa, Tadashi |
| contents | Cecotti and Vafa introduced the topological anti-topological fusion (tt*)-equation, whose solutions describe massive deformations of supersymmetric conformal field theories. We provide a rigorous analytic formulation of the $ADE$ classification of tt*-structures. Under natural structural assumptions, a tt*-structure over $\mathbb{C}^*$ can be described via isomonodromic deformations with upper unitriangular real Stokes matrices. Two fundamental issues arise: the ambiguities of Stokes matrices, governed by an action of a group $\tilde{Br}_n$, which is generated by reordering operations, and the solvability of the associated Riemann-Hilbert problem. Our first main result shows that the classification reduces to admissible Stokes matrices modulo $\tilde{Br}_n$-action, and that the $\tilde{Br}_n$-orbit of a Stokes matrix determines a tt*-structure over $\mathbb{C}^*$. Our second main result establishes that upper unitriangular matrices whose symmetrizations coincide with Cartan matrices of type $A_n, D_n, E_6, E_7,$ or $E_8$ give rise to tt*-structures over $\mathbb{C}^*$. This provides a direct analytic realization of the $ADE$ classification and clarifies the interplay between Stokes phenomena, $\tilde{Br}_n$-symmetry, and positivity of Cartan-type matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On tt*-structures from $ADE$-type Stokes data Udagawa, Tadashi Differential Geometry High Energy Physics - Theory 81T40, 34M40, 35Q15 Cecotti and Vafa introduced the topological anti-topological fusion (tt*)-equation, whose solutions describe massive deformations of supersymmetric conformal field theories. We provide a rigorous analytic formulation of the $ADE$ classification of tt*-structures. Under natural structural assumptions, a tt*-structure over $\mathbb{C}^*$ can be described via isomonodromic deformations with upper unitriangular real Stokes matrices. Two fundamental issues arise: the ambiguities of Stokes matrices, governed by an action of a group $\tilde{Br}_n$, which is generated by reordering operations, and the solvability of the associated Riemann-Hilbert problem. Our first main result shows that the classification reduces to admissible Stokes matrices modulo $\tilde{Br}_n$-action, and that the $\tilde{Br}_n$-orbit of a Stokes matrix determines a tt*-structure over $\mathbb{C}^*$. Our second main result establishes that upper unitriangular matrices whose symmetrizations coincide with Cartan matrices of type $A_n, D_n, E_6, E_7,$ or $E_8$ give rise to tt*-structures over $\mathbb{C}^*$. This provides a direct analytic realization of the $ADE$ classification and clarifies the interplay between Stokes phenomena, $\tilde{Br}_n$-symmetry, and positivity of Cartan-type matrices. |
| title | On tt*-structures from $ADE$-type Stokes data |
| topic | Differential Geometry High Energy Physics - Theory 81T40, 34M40, 35Q15 |
| url | https://arxiv.org/abs/2603.19871 |