A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d action is obtained from the 4d action by dimensional reduction up to terms which do not affect the exact results. By combining this fact and a recent proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a formula which gives the partition function depending on the Weyl weight of chiral multiplets, real mass parameters, FI parameters, and a squashing parameter as a limit of the index of a parent 4d theory.
In these lectures, we give a pedagogical introduction to the superconformal index. This is the writeup of the lectures given at the Winter School "YRISW 2020" and is to appear in a special issue of JPhysA. The lectures are at a basic level and are geared towards a beginning graduate student interested in working with the superconformal index.
从CP ^2 x R上的规范理论的指数出发，计算并研究了具有四个化学势的6dU（N）（2，0）理论的广义超共形指数.我们的指数与AdS_7 x S^4上低能时的大N超引力指数一致，并且还产生了具有N^3标度的负“卡西米尔能量”，这是最近根据S^5上的QFT计算出来的。我们的方法也建议系统的研究（1，0）超共形指数。
Bootstrapping the superconformal index with surface defects
N = 2的超共形指数的分析性质给出了物理解释的某些BPS表面缺陷，这是作为超对称涡的IR限制。味逸度中极点处的指数的留数被解释为没有这种味对称性的超共形场论的指数，但赋予了额外的表面缺陷。利用Ruijsenaars-Schneider型差分算子作用于该指数，可以有效地提取残差。通过施加的结合性约束的S-对偶，我们就能够评估指数的所有广义的A型理论，为通用值的三个超共形逸度，有或没有表面缺陷。
We show that the superconformal index of N=1 superconformal field theories in four dimensions has an asymptotic growth of states which is exponential in the charges. Our analysis holds in a Cardy-like limit of large charges, for which the index is dominated by small values of chemical potentials. In this limit we find the saddle points of the integral that defines the superconformal index using two different methods. One method, valid for finite N, is to first take the Cardy-like limit and then find the saddle points. The other method is to analyze the saddle points at large N and then take th…
We propose a prescription to calculate the superconformal index of the ${\cal N}=4$ $U(N)$ supersymmetric Yang-Mills theory with finite $N$ on the AdS side. The finite $N$ corrections are included as contributions of D3-branes wrapped around three-cycles in $\boldsymbol{S}^5$, which are calculated as the index of the gauge theories realized on the wrapped branes. The single-wrapping contribution has been studied in a previous work, and we further confirm that the inclusion of multiple-wrapping contributions correctly reproduces the higher order terms as far as we have checked numerically.
We compute superconformal indices for $\mathcal{N} = 3$ $\hat{ADE}$ Chern-Simons quiver gauge theories with a product gauge group $\prod_i U(N)_i$, using the method of supersymmetric localization. We also perform a large $N$ analysis of the index. This index includes contribution from non zero magnetic flux sector. The fact that these theories have a weakly coupled UV completion in terms of $\mathcal{N}= 3$ supersymmetric Chern-Simons Yang-Mills theories enables us to apply the localization technique. Such theories have dual M-theory description on $\mathrm{AdS}_4\times M_7$, where $M_7$ is a …
Finite $N$ Corrections to the Superconformal Index of S-fold Theories
利用AdS/CFT对应研究了S-折叠理论的超共形指数.已经知道，在大的$N$极限中的指数被再现为体卡鲁扎-克莱因模式的贡献。对于包裹在$\boldsymbol{S}^5/\mathbb{Z}_k$中的非平凡圈上的有限$N$ D 3-膜，对应于Pfidian-like算子，给出了阶$q^N$对指数的修正.我们通过分析包裹D3-膜的涨落来计算有限$N$修正。与已知结果的比较表明，我们的公式正确地再现了错误的顺序$q^{2N}$的校正。
We study the Cardy-like limit of the superconformal index of generic $\mathcal{N}=1$ SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugacities associated to angular momenta. The formula extends previous results valid at lowest order, and generalizes them to generic SCFTs. We corroborate the validity of our proposal by studying several examples, beyond the well-understood toric class. We compute the index also for models without a weakly-coupled gravity dual, whose gravitational anom…
We study the large-$N$ limit of superconformal index for two strongly interacting Chern-Simons theories in three dimensions with $\mathcal{N}=2$ supersymmetry, and compare the result against the AdS/CFT dual, namely the data of full Kaluza-Klein reduction spectra obtained using the exceptional field theory technique. The two theories of interest are mABJM and GJV theories, which are obtained as IR fixed point of RG whose UV description is ABJM and maximally supersymmetric Yang-Mills theory respectively. We confirm agreement and the duality persists. For the case of mABJM it turns out that we n…
