Open intersection numbers and free fields

Abstract

A complete set of the Virasoro and W-constraints for the Kontsevich-Penner model, which conjecturally describes intersections on moduli spaces of open curves, was derived in our previous work. Here we show that these constraints can be described in terms of free bosonic fields with twisted boundary conditions, which gives a modification of the well-known construction of the $W^{(3)}$ algebra in conformal field theory. This description is natural from the point of view of the spectral curve description, and should serve as a new important ingredient of the topological recursion/Givental decomposition.

21 pages; minor corrections, references added

References in corpus (4)

• Instantons and Merons in Matrix Models
• Enumerative geometry, tau-functions and Heisenberg-Virasoro algebra
• The combinatorial formula for open gravitational descendents
• Refined open intersection numbers and the Kontsevich-Penner matrix model

Cited by in corpus (10)

• Developments in Topological Gravity
• Refined open intersection numbers and the Kontsevich-Penner matrix model
• Quantization of Harer-Zagier formulas
• Higher Airy structures, W algebras and topological recursion
• Relations on ${\overline{\mathcal{M}}}_{g,n}$ and the negative $r$-spin Witten conjecture
• KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model
• On higher Brézin-Gross-Witten tau-functions
• From minimal gravity to open intersection theory
• KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions
• On affine coordinates of the tau-function for open intersection numbers