509 research outputs found
Open intersection numbers, Kontsevich-Penner model and cut-and-join operators
We continue our investigation of the Kontsevich--Penner model, which
describes intersection theory on moduli spaces both for open and closed curves.
In particular, we show how Buryak's residue formula, which connects two
generating functions of intersection numbers, appears in the general context of
matrix models and tau-functions. This allows us to prove that the
Kontsevich--Penner matrix integral indeed describes open intersection numbers.
For arbitrary we show that the string and dilaton equations completely
specify the solution of the KP hierarchy. We derive a complete family of the
Virasoro and W-constraints, and using these constraints, we construct the
cut-and-join operators. The case , corresponding to open intersection
numbers, is particularly interesting: for this case we obtain two different
families of the Virasoro constraints, so that the difference between them
describes the dependence of the tau-function on even times.Comment: 28 page
Open intersection numbers and free fields
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
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.Comment: 21 pages; minor corrections, references adde
From minimal gravity to open intersection theory
We investigated the relation between the two-dimensional minimal gravity
(Lee-Yang series) with boundaries and open intersection theory. It is noted
that the minimal gravity with boundaries is defined in terms of boundary
cosmological constant and the open intersection theory in terms of
boundary marked point generating parameter . Based on the conjecture that
the two different descriptions of the generating functions are related by the
Laplace transform, we derive the compact expressions for the generating
function of the intersection theory from that of the minimal gravity on a disk
and on a cylinder.Comment: 26 page
THE BUSINESS CYCLE AND ITS CONTEMPORARY CHARACTERISTICS
The article aims to present the business cycle phenomenon and its contemporary characteristics. Understanding the business cycle theory will allow for more in-depth research on this subject for the Bulgarian economy, through which to increase the macroeconomic efficiency of the country's economic polic
KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model
In this paper we introduce a new family of the KP tau-functions. This family
can be described by a deformation of the generalized Kontsevich matrix model.
We prove that the simplest representative of this family describes a generating
function of the cubic Hodge integrals satisfying the Calabi-Yau condition, and
claim that the whole family describes its generalization for the higher spin
cases. To investigate this family we construct a new description of the Sato
Grassmannian in terms of a canonical pair of the Kac-Schwarz operators.Comment: 83 pages, journal versio
KdV solves BKP
In this note, we prove that any tau-function of the KdV hierarchy also solves
the BKP hierarchy after a simple rescaling of times.Comment: 2 page
KP integrability of triple Hodge integrals. I. From Givental group to hierarchy symmetries
In this paper, we investigate a relation between the Givental group of rank
one and the Heisenberg-Virasoro symmetry group of the KP hierarchy. We prove,
that only a two-parameter family of the Givental operators can be identified
with elements of the Heisenberg-Virasoro symmetry group. This family describes
triple Hodge integrals satisfying the Calabi-Yau condition. Using the
identification of the elements of two groups we prove that the generating
function of triple Hodge integrals satisfying the Calabi-Yau condition and its
-version are tau-functions of the KP hierarchy. This generalizes the
result of Kazarian on KP integrability in the case of linear Hodge integrals.Comment: 32 pages, published versio
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