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

@article{Wang2022BKPHA,
  title={BKP hierarchy, affine coordinates, and a formula for connected bosonic n-point functions},
  author={Zhiyuan Wang and Chenglang Yang},
  journal={Letters in Mathematical Physics},
  year={2022}
}
. 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 [46]. Moreover, we prove a simple relation between the KP-affine coordinates of a tau-function τ ( t ) of the KdV hierarchy and the BKP-affine coordinates of τ ( t / 2). As applications, we present a new algorithm to compute the free energies of the Witten-Kontsevich tau-function and the Br… 

References

SHOWING 1-10 OF 55 REFERENCES

On affine coordinates of the tau-function for open intersection numbers

Cut-and-join description of generalized Brezin-Gross-Witten model

We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we

Generalized Br\'ezin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy

In this paper, we prove that the generalized Brézin–Gross–Witten taufunction is a hypergeometric solution of the BKP hierarchy with simple weight generating function. We claim that it describes a

Schur Q-Polynomials and Kontsevich-Witten Tau Function

Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau-function as a linear expansion of Schur Q-polynomials. In this paper, we will show directly that

Q-polynomial expansion for Brézin-Gross-Witten tau-function

Geometric interpretation of Zhou’s explicit formula for the Witten–Kontsevich tau function

Based on the work of Itzykson and Zuber on Kontsevich’s integrals, we give a geometric interpretation and a simple proof of Zhou’s explicit formula for the Witten–Kontsevich tau function. More

Tau Functions and their Applications

TLDR
This volume provides a thorough introduction to tau functions, starting from the basics and extending to recent research results, and is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tAU functions.

BKP hierarchy and Pfaffian point process

On fermionic representation of the framed topological vertex

A bstractThe Gromov-Witten invariants of ℂ3$$ {\mathbb{C}}^3 $$ with branes is encoded in the topological vertex which has a very complicated combinatorial expression. A simple formula for the

Topological Strings and Integrable Hierarchies

We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using -algebra symmetries which encode the symmetries of holomorphic
...