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Punctures and p-Spin Curves from Matrix Models II

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Abstract

We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to half-integer p, and in more details for \(p=\frac{1}{2}\) and \(p=\frac{3}{2}\). In those new cases one finds contributions from the Ramond sector, which were not present for positive integer p. The existence of Virasoro constraints, in particular a string equation, is considered also for half-integral spins. The contribution of the boundary of a Riemann surface, is investigated through a logarithmic matrix model. The supersymmetric random matrices provide extensions to mixed positive and negative p punctures.

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Acknowledgements

We are thankful to Edward Witten for the discussions about Ramond pair-wise punctures. We also thank referees for pointing out the relevant references and comments on the half-spin cases. S.H. is supported by JSPS KAKENHI 19H01813.

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Authors and Affiliations

  1. Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Kunigami, Okinawa, 904-0495, Japan

    S. Hikami

  2. Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005, Paris, France

    E. Brézin

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  1. S. Hikami
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  2. E. Brézin
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Correspondence to S. Hikami.

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Communicated by Irene Giardina.

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Hikami, S., Brézin, E. Punctures and p-Spin Curves from Matrix Models II. J Stat Phys 183, 36 (2021). https://doi.org/10.1007/s10955-021-02776-4

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