We study abelian and non-abelian orbifolds of the ABJM model. We compute the precise moduli space of these models by analyzing the classical BPS equations for the theory on the cylinder, which include classical solutions of magnetic monopole operators. These determine the chiral ring of the theory, and thus they provide the complete set of order parameters determining the classical vacua of the theory. We show that the proper quantization of these semiclassical solutions gives us the topology of moduli space, including the additional quotient information due to the Chern-Simons levels. In general, we find that in the dual M-theory setup, the M-theory fiber is divided by the product of the Chern-Simons level times the order of the orbifold group, even in the non-abelian case. This depends non-trivially on how the different Chern-Simons terms have different levels in these constructions. We also see a direct relation in this setup between the Chern-Simons levels of the different groups and fluxes for fractional brane cycles. We also show that the problem of the moduli space can be much more easily analyzed by using the method of images and representation theory of crossed product algebras rather than dealing only with the quiver theory data.
Integrable structure has played a very important role in the study of various non-perturbative aspects of planar ABJM theories. In this paper we showed that this remarkable structure survive after orbifold operation with discrete group $Γ(\simeq\mathbb{Z}_n)<SU(4)_R\times U(1)_b$. For general $Γ$, we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations. The eigenvalues of the anomalous dimension matrix are also obtained. For $Γ<SU(4)$, two-loop all-sector and all-loop BAEs are proposed. Supersymmetric orbifolds are discussed in this frame…
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the $d=3$ ${\mathcal N}=4$ super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition function of the ${\mathcal N}=4$ orbifold ABJM theory has been computed previously in the literature. In this paper, we re-derive it using a slightly different method. We calculate the vacuum expectation values of the circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2 BPS Wilson loops in arbitrary representations. We use both the…
Recently, ${\cal N} =3$ mass-deformed ABJM model with arbitrary mass-function depending on a spatial coordinate was constructed. In addition to the ${\cal N} = 3$ case, we construct lower supersymmetric ${\cal N} =1$ and ${\cal N} =2$ inhomogeneously mass-deformed ABJM (ImABJM) models, which require three and two arbitrary mass-functions, respectively. We also construct general vacuum solutions of the ${\cal N} = 3$ ImABJM model for any periodic mass-function. There are two classes of vacua, which are diagonal type and GRVV type according to reference value of mass-functions. We provide explic…
In this paper we construct and classify novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in $\mathcal N=2,3$ quiver superconformal Chern-Simons-matter theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and $\mathcal N=4$ orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and $\mathcal N=4$ orbifold ABJ…
In $\mathcal N \geq 2$ superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol'nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a supermatrix inside a superalgebra. However, for particular choices of the param…
In this paper we study non-commutative massive unquenched Chern-Simons matter theory using its gravity dual. We construct this novel background by applying a TsT-transformation on the known parent commutative solution. We discuss several aspects of this solution to the Type IIA supergravity equations of motion and, amongst others, check that it preserves ${\cal N}=1$ supersymmetry. We then turn our attention to applications and investigate how dynamical flavor degrees of freedom affect numerous observables of interest. Our framework can be regarded as a key step towards the construction of hol…
ABJM规范理论的Chern-Simons能级k描述了对偶几何中的轨道折叠。这表明，如果我们将膜从orbifold的尖端移到一个光滑的点，它应该会触发RG流，将IR中的水平改变为k=1。我们构造了一个显式的超重力解，该解与从通用k到k=1的这种转变是对偶的。在规范理论方面，我们提出的论点，为什么这种转变是合理的结束RG流。我们还考虑了k=4的情况下的轨道折叠的分辨率（可以找到显式度量），并构造了在AdS 4 X S7/Z4和AdS 4 X S7之间插值的光滑超引力解，对应于炸毁的六个周期上的局部化膜。在规范理论中，我们对与分辨对偶的四维算符以及相应的RG流作了一些评论。
Aspects of emergent geometry in the AdS/CFT context
我们研究的情况下，orbifold超共形场论在四维，其中的orbifolds是阿贝尔在AdS/CFT的建议紧急几何方面。特别地，我们表明，从N=4 SYM理论开始，在平坦空间中的单个D3膜的真空模空间中的粒子气体的涌现几何的实现被推广到相应的轨道共形场论的模空间上的粒子气体（轨道空间上的D3膜气体）。我们的主要目的是表明，这可以分析使用相同的技术，在N=4 SYM的情况下，通过使用图像的方法，包括测量的影响相关联的规范轨道的体积的配置。这种测度效应使粒子之间产生有效的排斥作用，使粒子凝聚成非平凡的真空位形，正是这些位形导致了AdS x X对偶场论中X的几何结构
To obtain a unified framework for symmetric and asymmetric heterotic orbifold constructions we provide a systematic study of Narain compactifications orbifolded by finite order T-duality subgroups. We review the generalized vielbein that parametrizes the Narain moduli space (i.e. the metric, the B-field and the Wilson lines) and introduce a convenient basis of generators of the heterotic T-duality group. Using this we generalize the space group description of orbifolds to Narain orbifolds. This yields a unified, crystallographic description of the orbifold twists, shifts as well as Narain modu…
We construct new families of 1/4 BPS Wilson loops in circular quiver $\mathcal N=4$ superconformal Chern-Simons-matter (SCSM) theories in three dimensions. They are defined as the holonomy of superconnections that contain non-trivial couplings to scalar and fermions, and cannot be reduced to block-diagonal matrices. Consequently, the new operators cannot be written in terms of double-node Wilson loops, as the ones considered so far in the literature. For particular values of the couplings the superconnection becomes block-diagonal and we recover the known fermionic 1/4 and 1/2 BPS Wilson loops…
We study non-BPS D-branes in the type II string vacua with chiral space-time SUSY constructed based on the asymmetric orbifolds of $\mbox{K3} \cong T^4/{\Bbb Z}_2$ as a succeeding work of arXiv:1704.05262[hep-th]. We especially focus on the fractional D-branes that contains the contributions from the twisted sector of the ${\Bbb Z}_2$ orbifolding. We show that the cylinder partition functions for these fractional branes do not vanish, as in the cases of ordinary non-BPS D-branes. This aspect is in a sharp contrast with the bulk-type branes studied in arXiv:1704.05262[hep-th]. We then discuss t…
我们讨论了紧致非交换卡-丘流形的代数几何方面。在这种情况下，考虑局部全纯代数是合适的，它们可以被粘合在一起成为一个紧的卡-丘代数。我们考虑两个例子：一个环面轨道折叠T^6/Z_2 x Z_2，和一个CP_4中五次轨道折叠，每个都有离散挠率。非对易几何工具足以描述轨道褶皱的各种性质。首先，我们正确地描述了膜在奇点处的分离。其次，对于第一个例子，我们表明，一个可以明确地恢复一个大切片的模空间的复杂结构变形的orbifold。对于这个例子，我们还表明，我们得到正确的计数复杂的结构变形的orbifold点，通过使用非交换微分形式（循环同源）的痕迹。
