Toda tau functions with quantum torus symmetries
Kanehisa Takasaki
TL;DR
This paper explores the role of quantum torus algebra in Toda hierarchy solutions, highlighting its realization via free fermions and its connection to topological strings and gauge theories.
Contribution
It introduces the realization of quantum torus algebra through free fermions and discusses its shift symmetries within Toda hierarchy solutions.
Findings
Quantum torus algebra underpins special Toda hierarchy solutions.
Connections established between quantum torus algebra, topological strings, and gauge theories.
Shift symmetries of the quantum torus algebra are analyzed.
Abstract
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.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons