The 2D Toda hierarchy occupies a central position in the family of integrable
hierarchies of the Toda type. The 1D Toda hierarchy and the Ablowitz-Ladik (aka
relativistic Toda) hierarchy can be derived from the 2D Toda hierarchy as
reductions. The...
The perspective of Kac-Schwarz operators is introduced to the authors'
previous work on the quantum mirror curves of topological string theory in
strip geometry and closed topological vertex. Open string amplitudes on each
leg of the web diagram o...
The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein ca...
Orbifold generalizations of the ordinary and modified melting crystal models are introduced. They are labelled by a pair of positive integers, and geometrically related to orbifolds of local g...
This paper addresses the issue of integrable structure in topological string
theory on generalized conifolds. Open string amplitudes of this theory can be
expressed as the matrix elements of an operator on the Fock space of 2D charged
free fermion...
A generating function of the single Hurwitz numbers of the Riemann sphere is a tau function of the lattice KP hierarchy. The associated
Lax operator turns out to be expressed as , where is a...
This paper addresses the problems of quantum spectral curves and 4D limit for the melting crystal model of 5D SUSY Yang-Mills theory on . The partition function deformed by an infinite number of exter...
J. Phys.: Conf. Ser. 482 (2014) 012041 2013年12月 [依頼有り]
This is a review of recent results on the integrable structure of the
ordinary and modified melting crystal models. When deformed by special external
potentials, the partition function of the ordinary melting crystal model is
known to become essen...
The notion of topological vertex and the construction of topological string
partition functions on local toric Calabi-Yau 3-folds are reviewed.
Implications of an explicit formula of partition functions for the generalized
conifolds are considered...
Seminar of IBS Center of Geometry and Physics 2018年3月27日 IBS Center of Geometry and Physics
The melting crystal model is a model of statistical mechanics
for random 3D Young diagrams. The partition function of this model
may be thought of as a -deformation of the generating function
of stationary Gromov-Witten invariants of $\mathbf{...
The melting crystal model is a model of statistical mechanics for random 3D Young diagrams. The partition function of this model may be thought of as a q-deformation of the generating function of stationary Gromov-Witten invariants of CP1 studied ...
Physics and Mathematics of Nonlinear Phenomena 2017年6月19日 B. Konopelchenko et al.
The melting crystal model is a toy model of Nekrasov's instanton partition functions for 5D supersymmetric gauge theories on R4 x S1. Its deformation by an infinite set of external potentials is known to become a tau function of the KP hierarchy. ...
The melting crystal model is a statistical model of 3D Young diagrams. Its partition function can be identified with the instanton partition function of 5D N = 1 supersymmetric U(1) Yang-Mills theory on R^4 × S^1. Its deformation by a set of exte...
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