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BKP hierarchy, affine coordinates, and a formula for connected bosonic n-point functions

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Abstract

We derive a formula for the connected n-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by Zhou (Emergent geometry and mirror symmetry of a point, 2015. arXiv:1507.01679). Moreover, we prove a simple relation between the KP-affine coordinates of a tau-function \(\tau (\varvec{t})\) of the KdV hierarchy and the BKP-affine coordinates of \(\tau (\varvec{t}/2)\). As applications, we present a new algorithm to compute the free energies of the Witten–Kontsevich tau-function and the Brézin–Gross–Witten tau-function.

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Acknowledgements

We thank the anonymous referees for suggestions. Z.W. thanks Professor Jian Zhou for helpful discussions and Professor Huijun Fan for encouragement. C.Y. thanks Professor Xiaobo Liu for patient guidance.

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  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Zhiyuan Wang

  2. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Chenglang Yang

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  1. Zhiyuan Wang
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Wang, Z., Yang, C. BKP hierarchy, affine coordinates, and a formula for connected bosonic n-point functions. Lett Math Phys 112, 62 (2022). https://doi.org/10.1007/s11005-022-01554-x

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