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<p>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.&#xa0;Hejhal and J.&#xa0;Fay relating Szegő kernels and Abelian differentials on Riemann surfaces, and a systematic use of operator product expansions both for the Ising and the bosonic correlations.</p>

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Bosonization of Primary Fields for the Critical Ising Model on Multiply Connected Planar Domains

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月1日

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  • Baran Bayraktaroglu,
  • Konstantin Izyurov,
  • Tuomas Virtanen,
  • Christian Webb

摘要

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 Szegő kernels and Abelian differentials on Riemann surfaces, and a systematic use of operator product expansions both for the Ising and the bosonic correlations.