Sammanfattning
We prove bosonization identities for the scaling limits of the critical Ising correlations in finitely-connected planar domains, expressing those in terms of correlations of the compactified Gaussian free field. This, in particular, yields explicit expressions for the Ising correlations in terms of domain's period matrix, Green's function, harmonic measures of boundary components and arcs, or alternatively, Abelian differentials on the Schottky double.
Our proof is based on a limiting version of a classical identity due to D. Hejhal and J. Fay relating Szegö kernels and Abelian differentials on Riemann surfaces, and a systematic use of operator product expansions both for the Ising and the bosonic correlations.
Our proof is based on a limiting version of a classical identity due to D. Hejhal and J. Fay relating Szegö kernels and Abelian differentials on Riemann surfaces, and a systematic use of operator product expansions both for the Ising and the bosonic correlations.
| Originalspråk | Engelska |
|---|---|
| Artikelnummer | 222 |
| Antal sidor | 58 |
| Tidskrift | Communications in Mathematical Physics |
| Volym | 406 |
| Nummer | 9 |
| DOI | |
| Status | Publicerad - sep. 2025 |
| MoE-publikationstyp | A1 Tidskriftsartikel-refererad |
Finansiering
Open Access funding provided by University of Helsinki (including Helsinki University Central Hospital). T.V. and C.W. were supported by the Emil Aaltonen Foundation. C.W. was supported by the Academy of Finland through the grant 348452. T.V. is also grateful for the financial support from the Doctoral Network in Information Technologies and Mathematics at Åbo Akademi University. B. B. and K.I. were supported by Academy of Finland through academy project “Critical phenomena in dimension two”. We are grateful to Mikhail Basok for useful remarks, as well as to two anonymous reviewers, whose careful reading and helpful comments have improved the article.