论文标题
不规则的共形块，PainlevéIII和爆炸方程
Irregular conformal blocks, Painlevé III and the blow-up equations
论文作者
论文摘要
我们研究了不规则的共形块与PainlevéIII$ _3 $方程的关系。证明准经典不规则块的功能表示与painlevéIII$ _3 $的BPZ方程和汉密尔顿 - 雅各比的方法一致。它立即导致了4D纯超对称仪表理论的双nekrasov分区函数的爆炸方程的限制案例，甚至可以将其视为$ c = 1 $和$ c \ to \ to \ to \ to \ to \ infty $共形块的定义方程式。我们将此分析扩展到了强耦合方案的领域，在该领域中，不知道保形块和Nekrasov函数的原始定义，并将结果应用于MathEIU方程的光谱问题。最后，我们通过量化PainlevéIII$ _3 $方程来构建强耦合区域中不规则的保形块，并以这种方式获得$ C = 1 $ c = 1 $ c = 1 $和Quasicalical $ c \ to \ infty $的一般表达。我们还发现了$ C = 1 $和$ c = -2 $的无限块的显式积分表示，对于某些特殊点。
We study the relation of irregular conformal blocks with the Painlevé III$_3$ equation. The functional representation for the quasiclassical irregular block is shown to be consistent with the BPZ equations of conformal field theory and the Hamilton-Jacobi approach to Painlevé III$_3$. It leads immediately to a limiting case of the blow-up equations for dual Nekrasov partition function of 4d pure supersymmetric gauge theory, which can be even treated as a defining system of equations for both $c=1$ and $c\to\infty$ conformal blocks. We extend this analysis to the domain of strong-coupling regime where original definition of conformal blocks and Nekrasov functions is not known and apply the results to spectral problem of the Matheiu equations. Finally, we propose a construction of irregular conformal blocks in the strong coupling region by quantization of Painlevé III$_3$ equation, and obtain in this way a general expression, reproducing $c=1$ and quasiclassical $c\to\infty$ results as its particular cases. We have also found explicit integral representations for $c=1$ and $c=-2$ irregular blocks at infinity for some special points.
