We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar field in five dimensions and admits a unique "deformation" which describes a massless conformal spinor. Scalar and spinor minreps of SO(5,2) are the 5d analogs of Dirac's singletons of SO(3,2). We then construct the minimal unitary representation of the unique 5d superconformal algebra F(4) with the even subalgebra SO(5,2) X SU(2). The minrep of F(4) describes a massless conformal supermultiplet consisting of two scalar and one spinor fields. We then extend our results to the construction of higher spin AdS_6/CFT_5 (super)-algebras. The Joseph ideal of the minrep of SO(5,2) vanishes identically as operators and hence its enveloping algebra yields the AdS_6/CFT_5 bosonic higher spin algebra directly. The enveloping algebra of the spinor minrep defines a "deformed" higher spin algebra for which a deformed Joseph ideal vanishes identically as operators. These results are then extended to the construction of the unique higher spin AdS_6/CFT_5 superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.
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.
AdS_3/CFT_2 Correspondence and Space-Time N=3 Superconformal Algebra
研究了目标空间为AdS_3 x（S^3 x S^3 x S^1）/Z_2的Wess-Zumino-Witten模型.这使我们能够构造时空N=3的超共形理论。通过GSO投影和Z_2投影将左、右运动部件组合起来，得到了一个新的非对称（N，\bar{N}）=（3，1）模型。它在IIA型弦的目标空间中具有额外的规范（仿射）SU（2）对称性。在M-理论观点中，一个相关构型被实现为与Z_2-固定平面斜交的M5-M2膜。
研究了玻色子空间的AdS_mxS ^n几何陪集超空间的超共形结构.特别地，我们证明了陪集流形AdS_2 x S^2，AdS_3 x S^3和AdS_5 x S^5的常规超空间扩张不是超共形平坦的，尽管它们的玻色子子流形是共形平坦的，这些超空间扩张是作为相应的D= 4，6，10超引力的解而产生的，并结合AdS/CFT对应得到了广泛的研究.我们给出了一个组理论推理这一事实。我们发现，在AdS_2 × S^2和AdS_3 × S^3情形下，存在不同的基于超群OSp（4^*）的超陪集|2）超共形平坦。我们还证明了在D= 2，3，4，5中存在超共形平坦的“纯”AdS_D超陪集.提出了超共形平坦性的两种检验方法。一种是求解Maurer-Cartan结构方程，另一种是将AdS_m x S^n超空间的等距超群嵌入到（m+n）维Minkowski空间的超共形群中.最后，我们讨论了上述结果在描述超对称动力系统中的一些应用。
Superconformal Algebras in Light-cone Gauge Quantization of String Theories on $AdS_3
受$AdS_3$上超弦理论的启发，我们构造了时空超共形代数（SCA），它们以横向物理自由度的形式存在于$AdS_3$边界上。所构造的SCA是N=4的大中代数和N=3的代数，分别对应于$AdS_3 \times S ^3 \times S^3 \times S ^1$、$AdS_3 \times S ^3 \times T ^4 $和$AdS_3 \times (S^3\times S^3\times S^1)/Z_2$背景上的超弦理论.
AdS Branes Corresponding to Superconformal Defects
在AdS/dCFT对应的背景下，研究了AdS_5 × X_5时空中的AdS_4 × L_2 D5-膜.这里X_5是Sasaki-Einstein流形，L_2是X_5的子流形.如果L_2是X_5中的一个特殊勒让德子流形，则这个膜具有与三维N=1超共形对称相同的超对称性。在这种情况下，这个膜应该对应于四维N=4的超杨-米尔斯理论中的超共形壁缺陷。我们构造了这些新的弦背景，并证明了它们具有正确的超对称性，在L_2上具有非平凡规范通量的情况下也是如此。最简单的新例子是AdS_5 x S^5中的AdS_4 x T^2膜。我们构建了膜的解决方案，表达RG流之间的两个不同的缺陷。我们还对AdS_4 x X_7中的AdS_3 x L_3 M5-膜，对弱G_2流形X_7及其子流形L_3进行了类似的分析。当L_3是结合子流形时，该系统具有与二维N=（1，0）整体超共形对称相同的超对称性.
The symmetric orbifold of $\mathbb{T}^4$ is the CFT dual of string theory on AdS$_3\times {\rm S}^3 \times \mathbb{T}^4$ with minimal NS-NS flux. We study its symmetry algebra and provide evidence that it does not have any deformation parameter. This suggests that the symmetric orbifold is (at least locally) the most symmetrical CFT in its moduli space.
We explicitly construct a family of ${\cal N}=4$ superconformal mechanics of dyonic particles, generalizing the work of Anninos et al.\,\cite{Anninos:2013nra} to an arbitrary number of particles. These mechanics are obtained from a scaling limit of the effective Coulomb branch description of ${\mathcal N}=4$ quiver quantum mechanics describing D-branes in type II Calabi-Yau compactifications. In the supergravity description of these D-branes this limit changes the asymptotics to AdS$_2\times $S$^2\times$CY$_3$. We exhibit the $D(1,2;0)$ superconformal symmetry and conserved charges of the mech…
In this letter we examine some structural aspects of the AdS/CFT such as the way of obtaining the expectation value of product of operators of the CFT, and ideas that should be considered when a proof of AdS/CFT is under consideration.
We calculate the superconformal indices of a class of six-dimensional ${\cal N}=(1,0)$ superconformal field theories realized on M5-branes at $\mathbb{C}^2/\mathbb{Z}_k$ singularity by using the method developed in previous works of the authors and collaborators. We use the AdS/CFT correspondence, and finite $N$ corrections are included as the contribution of M2-branes wrapped on two-cycles in $S^4/\mathbb{Z}_k$. We confirm that the indices are consistent with the expected flavor symmetries.
