Open KdV hierarchy of 2d minimal gravity of Lee-Yang series

Muraki, Hisayoshi; Rim, Chaiho

doi:10.1016/j.nuclphysb.2020.114971

Cited by 3 publications

(6 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This observation allows us to conjecture, that the s and µ B pictures are related by the Laplace (or Fourier) transform [5]…”

Section: Riemann Surfaces With Boundariesmentioning

confidence: 78%

“…Similar interplay is noted for the models on the Riemann surfaces with boundaries [4,5]. The GF of the MG with boundaries (BMG) satisfies the relations, similar to the ones known for the open intersection theory (OIT) [6].…”

Section: Introductionmentioning

confidence: 75%

“…where τ 0 -independent but τ n>0 -dependent contribution turns out to vanish except the trivial constant [5]. This solution can be compared with the GF of BMG from the matrix model com-…”

Section: Higherḡ-expansionmentioning

confidence: 95%

“…On the other hand, OIT and its open KdV are described by the boundary parameter s. As a result, the open KdV hierarchy of BMG differs from that of OIT. Nevertheless, the two different KdV hierarchies turn out to be closely related each other: Exponentials of the GF of two theories are related through the Laplace transform [5].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

From minimal gravity to open intersection theory

2019

Self Cite

View full text Add to dashboard Cite

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 µ B and the open intersection theory in terms of boundary marked point generating parameter s. 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.

show abstract

“…This observation allows us to conjecture, that the s and µ B pictures are related by the Laplace (or Fourier) transform [5]…”

Section: Riemann Surfaces With Boundariesmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 75%

“…where τ 0 -independent but τ n>0 -dependent contribution turns out to vanish except the trivial constant [5]. This solution can be compared with the GF of BMG from the matrix model com-…”

Section: Higherḡ-expansionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

From minimal gravity to open intersection theory

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…This gave rise to a flurry of mathematical activity which made earlier observations in the physics literature [13][14][15][16][17] precise [18][19][20][21]. See [22] for a partial review peppered with physical insight and [23][24][25] for more recent results.…”

Section: Introductionmentioning

confidence: 99%

Topological open/closed string dualities: matrix models and wave functions

Ashok

Troost²

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalized Kontsevich matrix model in the large dimension limit. We integrate out off-diagonal degrees of freedom associated to one source eigenvalue, and find an open/closed topological string partition function, thus proving open/closed duality. We match the resulting open partition function to the generating function of intersection numbers on moduli spaces of Riemann surfaces with boundaries and boundary insertions. Moreover, we connect our work to the literature on a wave function of the KP integrable hierarchy and clarify the role of the extended Virasoro generators that include all time variables as well as the coupling to the open string observable.

show abstract

Open minimal strings and open Gelfand-Dickey hierarchies

Aleshkin

Belavin

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the connection between minimal Liouville string theory and generalized open KdV hierarchies. We are interested in generalizing Douglas string equation formalism to the open topology case. We show that combining the results of the closed topology, based on the Frobenius manifold structure and resonance transformations, with the appropriate open case modification, which requires the insertion of macroscopic loop operators, we reproduce the well-known result for the expectation value of a bulk operator for the FZZT brane coupled to the general (q, p) minimal model. The matching of the results of the two setups gives new evidence of the connection between minimal Liouville gravity and the theory of Topological Gravity.

show abstract

Open KdV hierarchy of 2d minimal gravity of Lee-Yang series

Cited by 3 publications

References 42 publications

From minimal gravity to open intersection theory

From minimal gravity to open intersection theory

Topological open/closed string dualities: matrix models and wave functions

Open minimal strings and open Gelfand-Dickey hierarchies

Contact Info

Product

Resources

About