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arXiv · 2201.08178

BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions

Zhiyuan Wang·Chenglang Yang
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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 in [arXiv:1507.01679]. Moreover, we prove a simple relation between the KP-affine coordinates of a tau-function $\tau(\mathbf{t})$ of the KdV hierarchy and the BKP-affine coordinates of $\tau(\mathbf{t}/2)$. As applications, we present a new algorithm to compute the free energies of the Witten-Kontsevich tau-function and the Br\'ezin-Gross-Witten tau-function.

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Zhiyuan Wang, Chenglang Yang. 2022-01-20. BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions. https://doi.org/10.1007/s11005-022-01554-x

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