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 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 Brézin-Gross-Witten tau-function.

References in corpus (21)

• Topological Strings and Integrable Hierarchies
• Unitary matrix integrals in the framework of Generalized Kontsevich Model. I. Brezin-Gross-Witten Model
• Polynomial averages in the Kontsevich model
• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• Unitary And Hermitian Matrices In An External Field II: The Kontsevich Model And Continuum Virasoro Constraints
• Cut-and-join description of generalized Brezin-Gross-Witten model
• Superintegrability of Kontsevich matrix model
• The Adler-Shiota-van Moerbeke formula for the BKP hierarchy
• Polynomial tau-functions of BKP and DKP hierarchies
• Explicit Formula for Witten-Kontsevich Tau-Function
• Emergent Geometry and Mirror Symmetry of A Point
• Cut-and-join structure and integrability for spin Hurwitz numbers
• KdV solves BKP
• The n-point functions for intersection numbers on moduli spaces of curves
• BKP hierarchy and Pfaffian point process
• Hypergeometric functions related to Schur Q-polynomials and BKP equation
• Hermitian One-Matrix Model and KP Hierarchy
• K-Theory of Hilbert Schemes as a Formal Quantum Field Theory
• Grothendieck's Dessins d'Enfants in a Web of Dualities
• Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$
• On affine coordinates of the tau-function for open intersection numbers

Cited by in corpus (3)

• Kac-Schwarz Operators of Type $B$, Quantum Spectral Curves, and Spin Hurwitz Numbers
• Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected $(n,m)$-Point Functions, and Double Hurwitz Numbers
• Connected $(n,m)$-Point Functions of Diagonal $2$-BKP Tau-Functions, and Spin Double Hurwitz Numbers