scholarly journals Integrable structure of melting crystal model with external potentials

2019 ◽  
Author(s):  
Toshio Nakatsu ◽  
Kanehisa Takasaki
Keyword(s):  
Integrable Structure ◽  
Crystal Model ◽  
Melting Crystal

scholarly journals INTEGRABLE STRUCTURE OF 5d$\mathcal{N} = 1$ SUPERSYMMETRIC YANG-MILLS AND MELTING CRYSTAL

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2332-2342 ◽  
Author(s):  
TOSHIO NAKATSU ◽  
YUI NOMA ◽  
KANEHISA TAKASAKI
Keyword(s):  
Partition Function ◽  
Generating Function ◽  
Correlation Functions ◽  
External Potential ◽  
Yang Mills ◽  
Integrable Structure ◽  
Crystal Model ◽  
Melting Crystal ◽  
The Common

We study loop operators of 5d[Formula: see text] SYM in Ω background. Computation of their correlation functions is described. For the case of U(1) theory, the generating function reproduces the partition function of melting crystal model with external potential. We argue the common integrable structure of 5d[Formula: see text] SYM in Ω background and melting crystal model. An extension of the Seiberg-Witten geometry of the U(1) theory is presented.

scholarly journals Intertwining operator and integrable hierarchies from topological strings

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jean-Emile Bourgine
Keyword(s):  
Topological Strings ◽  
Vertex Operator ◽  
Integrable Hierarchies ◽  
Kp Hierarchy ◽  
Tau Function ◽  
Time Deformation ◽  
Toroidal Algebra ◽  
Crystal Model ◽  
Melting Crystal ◽  
Definition Of

Abstract In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the underlying quantum W1+∞ symmetry. Specifically, we point out the role played by automorphisms and the connection with the intertwiner — or vertex operator — of the algebra. This algebraic perspective allows us to extend part of their derivation to the refined melting crystal model, lifting the algebra to the quantum toroidal algebra of $$ \mathfrak{gl} $$ gl (1) (also called Ding-Iohara-Miki algebra). In this way, we take a first step toward the definition of deformed hierarchies associated to A-model refined topological strings.

scholarly journals Toda Tau Functions with Quantum Torus Symmetries

10.14311/1370 ◽  
2011 ◽  
Vol 51 (2) ◽  
Author(s):  
K. Takasaki
Keyword(s):  
Topological Strings ◽  
Special Class ◽  
Gauge Theories ◽  
Free Fermion ◽  
Fermion System ◽  
Quantum Torus ◽  
Tau Functions ◽  
Toda Hierarchy ◽  
Crystal Model ◽  
Melting Crystal

The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of topological strings and 5D SUSY gauge theories. The quantum torus algebra is realized by a 2D complex free fermion system that underlies the Toda hierarchy, and exhibits mysterious “shift symmetries”. This article is based on collaboration with Toshio Nakatsu.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model
Sign in / Sign up

Export Citation Format

Share Document