Research Paper#Theoretical Physics, Quantum Mechanics, Gauge Theory, Integrable Systems🔬 ResearchAnalyzed: Jan 3, 2026 16:38
Bilinear Forms and Blowup Relations in Quantum Painlevé Equations and SUSY Gauge Theories
Analysis
This paper connects the mathematical theory of quantum Painlevé equations with supersymmetric gauge theories. It derives bilinear tau forms for the quantized Painlevé equations, linking them to the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in gauge theory partition functions. The paper also clarifies the relationship between the quantum Painlevé Hamiltonians and the symmetry structure of the tau functions, providing insights into the gauge theory's holonomy sector.
Key Takeaways
- •Establishes a connection between quantum Painlevé equations and supersymmetric gauge theories.
- •Derives bilinear tau forms for quantum Painlevé equations.
- •Clarifies the relationship between quantum Painlevé Hamiltonians and tau function symmetry.
- •Provides insights into the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in the nontrivial holonomy sector of gauge theory.
Reference
“The paper derives bilinear tau forms of the canonically quantized Painlevé equations, relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations.”