从5维规范理论中自举离散Painlevé系统的双线性关系
Bootstrapping bilinear relations of discrete Painlevé systems from 5d gauge theories
AI总结：
该研究通过5维N=1超对称场论与Painlevé方程的对应关系，提出自举方法确定τ函数双线性关系，应用于SU(2)规范理论得到对应方程的双线性关系，且可推广至其他5维超对称场论。
AI中文摘要：
我们通过椭圆Painlevé方程和q-Painlevé方程与5维N=1超对称场论的对应关系，研究其τ函数。以Ω背景下配分函数的形式定义与5维场论相关的τ函数，我们提出一种自举方法，该方法可结合有效预势、微扰贡献及理论的整体对称性，确定τ函数的双线性关系。将该方法应用于耦合了N_f≤8个基本超多重态的5维SU(2)规范理论，我们得到了椭圆Painlevé方程和q-Painlevé方程的双线性关系。该方法还可应用于SU(2)规范理论之外的一般5维超对称场论。
英文摘要：
We study tau-functions of elliptic and $ q $-Painlevé equations through their correspondence with 5d $ \mathcal{N}=1 $ supersymmetric field theories. Defining tau-functions associated with 5d field theories in terms of partition functions on the $ Ω$-background, we propose a bootstrap method that determines their bilinear relations from the effective prepotential and the perturbative contributions, together with the global symmetry of the theory. Applying the method to 5d $ \mathrm{SU}(2) $ gauge theories coupled to $ N_f \leq 8 $ fundamental hypermultiplets, we obtain the bilinear relations of the elliptic and $ q $-Painlevé equations. This method can be applied to general 5d supersymmetric field theories beyond $ \mathrm{SU}(2) $ gauge theories.
