Virasoro constraints and polynomial recursion for the linear Hodge integrals

Guo, Shuai; Wang, Gehao

doi:10.1007/s11005-016-0923-x

Cited by 6 publications

(4 citation statements)

References 32 publications

(83 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Examples about the conjugation of Heisenberg-Virasoro operators on constraints can be found in other articles such as [12] and [5].…”

Section: Jhep03(2023)215mentioning

confidence: 99%

The ordered exponential representation of GKM using the W1+∞ operator

Wang

2023

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an r-reduced tau-function that governs the r-spin intersection numbers. In this paper, we present an ordered exponential representation of monomial GKM in terms of the W1+∞ operators that preserves the KP integrability. In fact, this representation is naturally the solution of a W1+∞ constraint that uniquely determines the tau-function. Furthermore, we show that, for the cases of Kontsevich-Witten and generalized BGW tau-functions, their W1+∞ representations can be reduced to their cut-and-join representations under the reduction of the even time independence and Virasoro constraints.

show abstract

“…Examples about the conjugation of Heisenberg-Virasoro operators on constraints can be found in other articles such as [12] and [5].…”

Section: Jhep03(2023)215mentioning

confidence: 99%

The ordered exponential representation of GKM using the W1+∞ operator

Wang

2023

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the case of linear Hodge integrals (p = 0, α = 1) the Heisenberg-Virasoro constraints were derived in [Ale15]. A more convenient basis of constraints was obtained in [GW17]. Constraints in Theorem 1 provide a generalization of this basis for arbitrary p and α ∈ {0, 1}.…”

Section: Heisenberg-virasoro and Dimension Constraintsmentioning

confidence: 99%

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

Alexandrov

2021

Preprint

View full text Add to dashboard Cite

In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi-Yau condition. For the tau-functions, which generate these integrals, we derive the complete families of the Heisenberg-Virasoro constraints. We also construct several equivalent versions of the cut-and-join operators. These operators describe the algebraic version of topological recursion. For the specific values of parameters associated with the KdV reduction, we prove that these tau-functions are equal to the generating functions of intersection numbers of ψ and κ classes. We interpret this relation as a symplectic invariance of the Chekhov-Eynard-Orantin topological recursion and prove this recursion for the general Θ-case.

show abstract

“…As one of the many examples, in [8], these commutator relations are the crucial part in the proof of the equivalence relations among the Virasoro constraints, cutand-join equation and polynomial recursion relation for the linear Hodge integrals using the main formula in [13]. In the paper [1], Alexandrov posted a conjecture stating that there exists a GL(∞) operator consisting of only the Virasoro operators that connects the Hodge tau-function τ Hodge and Kontsevich tau-function τ KW .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%