Irregular conformal blocks and connection formulae for Painlev\'e V functions
| Autor: | Lisovyy, O., Nagoya, H., Roussillon, J. |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.5031841 |
| Popis: | We prove a Fredholm determinant and short-distance series representation of the Painlev\'e V tau function $\tau(t)$ associated to generic monodromy data. Using a relation of $\tau(t)$ to two different types of irregular $c=1$ Virasoro conformal blocks and the confluence from Painlev\'e VI equation, connection formulas between the parameters of asymptotic expansions at $0$ and $i\infty$ are conjectured. Explicit evaluations of the connection constants relating the tau function asymptotics as $t\to 0,+\infty,i\infty$ are obtained. We also show that irregular conformal blocks of rank 1, for arbitrary central charge, are obtained as confluent limits of the regular conformal blocks. Comment: 26 pages, 1 figure |
| Databáze: | arXiv |
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