• Corpus ID: 245424618

On the Hodge-BGW correspondence

@inproceedings{Yang2021OnTH,
  title={On the Hodge-BGW correspondence},
  author={Di Yang and Qingsheng Zhang},
  year={2021}
}
We establish an explicit relationship between the partition function of certain special cubic Hodge integrals and the generalized Brézin–Gross–Witten (BGW) partition function, which we refer to as the Hodge-BGW correspondence. As an application, we obtain an ELSV-like formula for generalized BGW correlators. 
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3 Citations

3 Citations

Citation Type

Citation Type

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References

SHOWING 1-10 OF 62 REFERENCES
Hodge–GUE Correspondence and the Discrete KdV Equation
We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mari\~no--Vafa type [17, 28] and GUE correlators, and the conjecture…
The Hodge-FVH correspondence
TLDR
A gap condition is proved for certain special cubic Hodge integrals and an algorithm is given for computing the coefficients that appear in the gap condition.
Hodge Integrals and Integrable Hierarchies
We show that the generating series of some Hodge integrals involving one or two partitions are τ-functions of the KP hierarchy or the 2-Toda hierarchy, respectively. We also reformulate the results…
On cubic Hodge integrals and random matrices
A conjectural relationship between the GUE partition function with even couplings and certain special cubic Hodge integrals over the moduli spaces of stable algebraic curves is under consideration.
Fractional Volterra hierarchy
The generating function of cubic Hodge integrals satisfying the local Calabi–Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a fractional…
On tau-functions for the KdV hierarchy
For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic…
On Itzykson-Zuber Ansatz
Abstract We apply the renormalized coupling constants and Virasoro constraints to derive the Itzykson-Zuber Ansatz on the form of the free energy in 2D topological gravity. We also treat the 1D…
KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions
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…
A formula of two-partition Hodge integrals
JMg,n where tpi = ci(L?) is the first Chern class of L?, and Xj = Cj(E) is the j-th Chern class of the Hodge bundle. The study of Hodge integrals is an important part of intersection theory on Mg,n>…
A Proof of a Conjecture of Marino-Vafa on Hodge Integrals
We prove a remarkable formula for Hodge integrals conjectured by Marino and Vafa based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms.
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