论文标题
超符号指数中的子领导结构：次要马鞍和对数贡献
Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
论文作者
论文摘要
我们在$ {\ cal n} = 4 $ SU（$ n $）量规组的$ {\ cal n} = 4 $ supersymmetratric yang-mills理论的超符号指数中系统地研究各种子领先结构。我们集中于超符号索引描述作为椭圆伽玛函数的矩阵模型和伯特 - 阿萨茨的呈现。我们的鞍点近似超出了类似心脏的限制，我们发现了与SU（$ n $）Chern-Simons理论相对应的矩阵模型控制的各种马鞍。然而，主导的马鞍与伯特 - 萨茨的方法达成了完全同意。我们还确定对超符号索引的对数校正为$ \ log n $，在各自的近似值中找到了鞍点和伯特 - 阿萨茨之间的精确协议。我们概括了两种方法，以涵盖大型的4D $ {\ cal n} = 1 $ supercongon -grom -grom -grom -grom -grongulal Theories。我们发现，在这种情况下，这两个近似都一致，直到表格$ \ log n $的通用贡献。最后一个结果的普遍性构成了这种渐近广告的紫外线描述的强大签名，可以通过低能IIB超级重力进行测试。
We systematically study various sub-leading structures in the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills theory with SU($N$) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU($N$) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be $\log N$, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d ${\cal N}=1$ superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form $\log N$. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS$_5$ black holes and could be tested by low-energy IIB supergravity.
