本文研究了最近在arXiv：0809.3237中引入的N=2超对称Chern-Simons规范规范理论，该理论描述了著名的Sasaki-Einstein流形Q^{1，1，1}上的锥上的M2-膜.对于Chern-Simons能级（k，k，-k，-k），我们证明了该理论与AdS_4 x Q^{1，1，1}/Z_k是对偶的.我们导出了Z_k轨道作用量，并证明它保持几何对称性U（1）_R × SU（2）× U（1），这与规范理论的对称性是一致的。我们分析了最简单的规范不变手征算符，证明了它们与AdS_4 x Q^{1，1，1}/Z_k上的Kaluza-Klein调和函数相匹配.这提供了一个测试的规范理论，特别是它的六次超势发挥了重要作用，限制频谱的手征运营商。我们接着研究与更复杂的Q^{1，1，1}轨道相对应的其他量子规范理论。特别地，我们提出了两个U（N）^4陈-西蒙斯规范理论，它们的图与描述F_0上复锥上D3-膜的4d理论中的图相同，F_0是锥的Z_2轨道（在4d中，两个箭图通过塞伯格对偶联系起来）。这些规范理论的明显对称性是U（1）_R × SU（2）× SU（2）。证明了（k，k，-k，-k）能级上的规范理论与AdS_4 x Q^{2，2，2}/Z_k是对偶的.我们展示了计算的模空间和手征运营商的频谱提供支持这一猜想。我们还简要地讨论了AdS_4 × M^{3，2}/Z_k的一个类似对应。最后，我们讨论了锥的分解及其对偶规范理论。
英文摘要：
We study the N=2 supersymmetric Chern-Simons quiver gauge theory recently introduced in arXiv:0809.3237 to describe M2-branes on a cone over the well-known Sasaki-Einstein manifold Q^{1,1,1}. For Chern-Simons levels (k,k,-k,-k) we argue that this theory is dual to AdS_4 x Q^{1,1,1}/Z_k. We derive the Z_k orbifold action and show that it preserves geometrical symmetry U(1)_R x SU(2) x U(1), in agreement with the symmetry of the gauge theory. We analyze the simplest gauge invariant chiral operators, and show that they match Kaluza-Klein harmonics on AdS_4 x Q^{1,1,1}/Z_k. This provides a test of the gauge theory, and in particular of its sextic superpotential which plays an important role in restricting the spectrum of chiral operators. We proceed to study other quiver gauge theories corresponding to more complicated orbifolds of Q^{1,1,1}. In particular, we propose two U(N)^4 Chern-Simons gauge theories whose quiver diagrams are the same as in the 4d theories describing D3-branes on a complex cone over F_0, a Z_2 orbifold of the conifold (in 4d the two quivers are related by the Seiberg duality). The manifest symmetry of these gauge theories is U(1)_R x SU(2) x SU(2). We argue that these gauge theories at levels (k,k,-k,-k) are dual to AdS_4 x Q^{2,2,2}/Z_k. We exhibit calculations of the moduli space and of the chiral operator spectrum which provide support for this conjecture. We also briefly discuss a similar correspondence for AdS_4 x M^{3,2}/Z_k. Finally, we discuss resolutions of the cones and their dual gauge theories.
详细分析了有挠和无挠的轨道理论中D-膜对开弦的轨道作用的一致性。以C^3/Z_2 x Z_2理论为例，我们发现轨道作用量的相容性要求D-膜谱既包含产生轨道群的传统表示的膜，也包含表示是投射的膜。本文还展示了这些结果如何推广到C^3/Z_N × Z_N的轨道折叠上，并由此产生了许多新的特征.特别地，具有最小离散挠率的N>2理论具有在扭曲R-R势下带电的非BPS膜，该扭曲R-R势与任何（已知的）BPS膜都不耦合。
Non-BPS D-brane Solutions in Six Dimensional Orbifolds
从Eyras和Panda最近构造的IIB/ $(-1)^{F_L}I_4$的非BPS D 0-膜解出发，利用T-对偶构造了Sen预言的IIB/ $(-1)^{F_L}I_4$和IIA/ $(-1)^{F_L}I_4$的非BPS D 2-膜和D 1-膜解。而D1-膜耦合（电和磁）到NS 5A-膜的自对偶2-形式的潜力，这是目前在IIA型orbifold结构的扭曲部门。最后，我们讨论了这些膜的11维解释，起源于一个非BPS的M-理论定向折叠的$Ω_ρI_5$的M1-膜的解决方案。
We study the type II string vacua with chiral space-time SUSY constructed as asymmetric orbifolds of torus and $ K3 $ compactifications. Despite the fact that all the D-branes are non-BPS in any chiral SUSY vacua, we show that the relevant non-geometric vacua of asymmetric orbifolds allow rather generally configurations of D-branes which lead to vanishing cylinder amplitudes, implying the bose-fermi cancellation at each mass level of the open string spectrum. After working on simple models of toroidal asymmetric orbifolds, we focus on the asymmetric orbifolds of $ T^2 \times {\cal M} $, where …
我们系统地重新审视了轨道折叠上的$D$ -膜的描述以及通过K-理论对其电荷的分类。我们包括足够的细节，使结果访问物理学家和数学家感兴趣的这些主题。在Z_N轨道折叠中，K-理论预言的具有$N$奇数的最小荷电膜只有BPS。我们用Z_3的边界态形式证实了这一结果。对于有和没有离散挠率的Z_N x Z_N轨道，我们证明了电荷的K-理论分类与边界态方法一致，包括Chan-Paton因子的表示类型。
D3 branes in the vicinity of an E6, E7, or E8 stack of 7-branes in flat space are known to host at low energy a famous class of strongly-coupled N = 2 superconformal field theories featuring exceptional global symmetry. What if, instead, the 7-branes wrap an orbifold? We give a systematic characterization of such theories in the case of C2/Zn, and determine their main properties, like global symmetries, spectra of Coulomb-branch operators, and patterns of Higgs-branch flows. We put forward a set of rules to construct their magnetic quivers, which directly generalize what happens in the perturb…
We introduce Orbifold Reduction, a new method for generating $2d$ $(0,2)$ gauge theories associated to D1-branes probing singular toric Calabi-Yau 4-folds starting from $4d$ $\mathcal{N}=1$ gauge theories on D3-branes probing toric Calabi-Yau 3-folds. The new procedure generalizes dimensional reduction and orbifolding. In terms of T-dual configurations, it generates brane brick models starting from brane tilings. Orbifold reduction provides an agile approach for generating $2d$ $(0,2)$ theories with a brane realization. We present three practical applications of the new algorithm: the connecti…
