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

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.