论文标题
关于Nekrasov功能的收敛性
On the convergence of Nekrasov functions
论文作者
论文摘要
在本说明中，我们介绍了Nekrasov分区的收敛性的一些结果，在Instanton Counting参数中充当功率序列。 We focus on $U(N)$ ${\mathcal N}=2$ gauge theories in four dimensions with matter in the adjoint and in the fundamental representations of the gauge group respectively and find rigorous lower bounds for the convergence radius in the two cases: if the theory is {\it conformal}, then the series has at least a {\it finite} radius of convergence, while if it is {\ IT渐近自由}它具有{\ it Infinite}收敛半径。通过AGT对应关系，这意味着$ W_N $代数的相关不规则的保形块接收在整个平面中收敛的模量中的功率扩展。通过指定$ su（2）$案例，我们应用结果来分析相应的painlevé$τ$函数的收敛属性。
In this note we present some results on the convergence of Nekrasov partition functions as power series in the instanton counting parameter. We focus on $U(N)$ ${\mathcal N}=2$ gauge theories in four dimensions with matter in the adjoint and in the fundamental representations of the gauge group respectively and find rigorous lower bounds for the convergence radius in the two cases: if the theory is {\it conformal}, then the series has at least a {\it finite} radius of convergence, while if it is {\it asymptotically free} it has {\it infinite} radius of convergence. Via AGT correspondence, this implies that the related irregular conformal blocks of $W_N$ algebrae admit a power expansion in the modulus converging in the whole plane. By specifying to the $SU(2)$ case, we apply our results to analyse the convergence properties of the corresponding Painlevé $τ$-functions.
