论文标题
残留物，模块化和4D $ \ MATHCAL {N} = 4 $ SUPERCONGUN -SUPERCONTOR INDEX的CARDY极限
Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
论文作者
论文摘要
我们通过残基计算计算$ \ Mathcal {n} = 4 $ $ su（n）$ yang-mills理论的超符号索引。该方法在精神上与伯特·安萨兹形式主义相似，除了明确知道所有极点，而且我们不需要对任何化学潜力的专业化。我们的索引表达式使我们能够使用四维超对称分区函数的模块化特性重新审视Cardy极限。我们发现所有残留物在CARDY限制下以领先顺序贡献。在特定的风味化学潜力空间中，接近两个未精制的点，实际上所有残基都普遍贡献。这些通用残基完全与渐近广告的熵函数分别一致。最后，我们讨论了如何适合研究四维模块化对索引超出基础极限的索引的含义。
We compute the superconformal index of the $\mathcal{N}=4$ $SU(N)$ Yang-Mills theory through a residue calculation. The method is similar in spirit to the Bethe Ansatz formalism, except that all poles are explicitly known, and we do not require specialization of any of the chemical potentials. Our expression for the index allows us to revisit the Cardy limit using modular properties of four-dimensional supersymmetric partition functions. We find that all residues contribute at leading order in the Cardy limit. In a specific region of flavour chemical potential space, close to the two unrefined points, in fact all residues contribute universally. These universal residues precisely agree with the entropy functions of the asymptotically AdS$_5$ black hole and its "twin saddle" respectively. Finally, we discuss how our formula is suited to study the implications of four-dimensional modularity for the index beyond the Cardy limit.
