467 citations · 2k across the 86 of their papers we have counts for
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Extended Seiberg-Witten Theory and Melting Crystal
Toshio Nakatsu, Yui Noma, Kanehisa Takasaki
We study an extension of the Seiberg-Witten theory of supersymmetric Yang-Mills on . We investigate correlation functions among loop o…
Integrable Structure of Supersymmetric Yang-Mills and Melting Crystal
Toshio Nakatsu, Yui Noma, Kanehisa Takasaki
We study loop operators of SYM in background. For the case of U(1) theory, the generating function of correlation functions of the loop operators reproduce…
Melting Crystal, Quantum Torus and Toda Hierarchy
Toshio Nakatsu, Kanehisa Takasaki
Searching for the integrable structures of supersymmetric gauge theories and topological strings, we study melting crystal, which is known as random plane partition, from the viewp…
Explicit solutions of the classical Calogero & Sutherland systems for any root system
R. Sasaki, K. Takasaki
Explicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalisation of…
Free Fermion and Seiberg-Witten Differential in Random Plane Partitions
Takashi Maeda, Toshio Nakatsu, Kanehisa Takasaki +1
A model of random plane partitions which describes five-dimensional supersymmetric SU(N) Yang-Mills is studied. We compute the wave functions of fermions in this st…
Five-Dimensional Supersymmetric Yang-Mills Theories and Random Plane Partitions
Takashi Maeda, Toshio Nakatsu, Kanehisa Takasaki +1
Five-dimensional supersymmetric Yang-Mills theories are investigated from the viewpoint of random plane partitions. It is shown that random plane partitions are fac…
Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
R. Sasaki, K. Takasaki
Inozemtsev models are classically integrable multi-particle dynamical systems related to Calogero-Moser models. Because of the additional q^6 (rational models) or sin^2(2q) (trigon…
Anti-self-dual Yang-Mills equations on noncommutative spacetime
Kanehisa Takasaki
By replacing the ordinary product with the so called -product, one can construct an analogue of the anti-self-dual Yang-Mills (ASDYM) equations on the noncommutative $\bbR^4…
Calogero-Moser Models IV: Limits to Toda theory
S. P. Khastgir, R. Sasaki, K. Takasaki
Calogero-Moser models and Toda models are well-known integrable multi-particle dynamical systems based on root systems associated with Lie algebras. The relation between these two…
Whitham Deformations and Tau Functions in N = 2 Supersymmetric Gauge Theories
Kanehisa Takasaki
We review new aspects of integrable systems discovered recently in N=2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit c…
Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups
Kanehisa Takasaki
Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $\calN = 2$ SUSY Yang-Mills theory. We extend their result to…
Calogero-Moser Models II: Symmetries and Foldings
A. J. Bordner, R. Sasaki, K. Takasaki
Universal Lax pairs (the root type and the minimal type) are presented for Calogero-Moser models based on simply laced root systems, including E_8. They exist with and without spec…
Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
Kanehisa Takasaki
The -plane integrals of topologically twisted supersymmetric gauge theories generally contain contact terms of nonlocal topological observables. This paper proposes an i…
Gaudin Model, KZ Equation, and Isomonodromic Problem on Torus
Kanehisa Takasaki
This paper presents a construction of isospectral problems on the torus. The construction starts from an SU(n) version of the XYZ Gaudin model recently studied by Kuroki and Takebe…
Isomonodromic deformations and supersymmetric gauge theories
Kanehisa Takasaki, Toshio Nakatsu
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy p…
Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory
Toshio Nakatsu, Kanehisa Takasaki
The exact solution of supersymmetric Yang-Mills theory is studied in the framework of the Whitham hierarchies. The solution is identified with a homogeneous solution…
Toda Lattice Hierarchy and Generalized String Equations
Kanehisa Takasaki
String equations of the -th generalized Kontsevich model and the compactified string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to…
Symmetries and tau function of higher dimensional dispersionless integrable hierarchies
Kanehisa Takasaki
A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional ``phase space'' variables of the dispersionless KP hierar…
Integrable Hierarchies and Dispersionless Limit
Kanehisa Takasaki, Takashi Takebe
Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as…
Dispersionless Toda hierarchy and two-dimensional string theory
Kanehisa Takasaki
The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification ra…
Nonabelian KP hierarchy with Moyal algebraic coefficients
Kanehisa Takasaki
A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new…
Integrable hierarchy underlying topological Landau-Ginzburg models of D-type
Kanehisa Takasaki
A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-tye is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (``…
Quasi-classical limit of BKP hierarchy and W-infinity symmeties
Kanehisa Takasaki
Previous results on quasi-classical limit of the KP and Toda hierarchies are now extended to the BKP hierarchy. Basic tools such as the Lax representation, the Baker-Akhiezer funct…
Quasi-classical limit of Toda hierarchy and W-infinity symmetries
Kanehisa Takasaki, Takashi Takebe
Previous results on quasi-classical limit of the KP hierarchy and its W-infinity symmetries are extended to the Toda hierarchy. The Planck constant now emerges as the spaci…