Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913078462906368 |
|---|---|
| author | Das, Arpit Mukhi, Sunil |
| author_facet | Das, Arpit Mukhi, Sunil |
| contents | Rational conformal field theories in 2d have partition functions built from holomorphic characters, whose classification can be addressed via the holomorphic modular bootstrap. This is facilitated by a special basis of ``quasi-characters'' that has been completely classified for rank-2. Suitably combining these to form admissible characters with non-negative integral coefficients $a_n$ depends crucially on the signs and growth of the quasi-character coefficients. We use Frobenius recursion relations for Modular Linear Differential Equations to estimate the growth with $c$ of these coefficients in the region $n\sim\frac{c}{12}$ that is inaccessible to Cardy asymptotics, and to prove rigorously that they have alternating signs that stabilise to a fixed sign at this order. This provides a practical path to obtain candidate RCFT partition functions at arbitrary Wronskian index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT Das, Arpit Mukhi, Sunil High Energy Physics - Theory Mathematical Physics Number Theory Quantum Algebra Representation Theory Rational conformal field theories in 2d have partition functions built from holomorphic characters, whose classification can be addressed via the holomorphic modular bootstrap. This is facilitated by a special basis of ``quasi-characters'' that has been completely classified for rank-2. Suitably combining these to form admissible characters with non-negative integral coefficients $a_n$ depends crucially on the signs and growth of the quasi-character coefficients. We use Frobenius recursion relations for Modular Linear Differential Equations to estimate the growth with $c$ of these coefficients in the region $n\sim\frac{c}{12}$ that is inaccessible to Cardy asymptotics, and to prove rigorously that they have alternating signs that stabilise to a fixed sign at this order. This provides a practical path to obtain candidate RCFT partition functions at arbitrary Wronskian index. |
| title | Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT |
| topic | High Energy Physics - Theory Mathematical Physics Number Theory Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2507.07170 |