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首页> 外文期刊>The journal of high energy physics >Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
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Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function

机译：Shiraishi功能的椭圆升降机作为非静止双椭圆功能

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A bstract As a development of [1], we note that the ordinary Shiraishi functions have an insufficient number of parameters to describe generic eigenfunctions of double elliptic system (Dell). The lacking parameter can be provided by substituting elliptic instead of the ordinary Gamma functions in the coefficients of the series. These new functions (ELS-functions) are conjectured to be functions governed by compactified DIM networks which can simultaneously play the three roles: solutions to non-stationary Dell equations, Dell conformal blocks with the degenerate field (surface operator) insertion, and the corresponding instanton sums in 6 d SUSY gauge theories with adjoint matter. We describe the basics of the corresponding construction and make further conjectures about the various limits and dualities which need to be checked to make a precise statement about the Dell description by double-periodic network models with DIM symmetry. We also demonstrate that the ELS-functions provide symmetric polynomials, which are an elliptic generalization of Macdonald ones, and compute the generation function of the elliptic genera of the affine Laumon spaces. In the particular U(1) case, we find an explicit plethystic formula for the 6 d partition function, which is a non-trivial elliptic generalization of the ( q, t ) Nekrasov-Okounkov formula from 5 d .
机译：Bstract作为[1]的发展，我们注意到普通的Shiraishi功能具有不足的参数数量来描述双椭圆系统（戴尔）的通用特征功能。可以通过在系列的系数中代替椭圆形而不是普通的伽马功能来提供缺少的参数。这些新功能（ELS-Functions）被猜测是由压缩暗淡网络控制的功能，可以同时播放三个角色：非静止戴尔方程的解决方案，Dell共形块与退化场（表面操作员）插入，以及相应的在6个D Susy Cauge理论中的算法总和伴随着伴随物质。我们描述了相应施工的基础知识，并进一步猜测需要检查的各种限制和二元性，以通过具有昏暗对称的双周期性网络模型对戴尔描述进行精确陈述。我们还证明了ELS函数提供了对称多项式，这是麦克唐纳的椭圆概括，并计算辐射劳斯空间的椭圆形属的产生功能。在特定的U（1）案例中，我们发现了6D分区功能的显式血浆公式，这是（Q，T）Nekrasov-Okounkov公式的非平凡椭圆概括。

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