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arXiv 1502.03281hep-thgr-qc
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AdS_4 × S^7/Z_k上M-膜的对偶局部化对象

Dual Localized Objects From M-Branes Over AdS_4 x S^7/Z_k

M. Naghdi

备注：
20 pages, than the v2 version: minor changes, some discussions improved, references added and typos fixed
发表信息：
Class. Quantum Grav. 32, 215018 (2015)
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摘要：

在保持几何不变的前提下，我们考虑了AdS_4 × S^7/Z_k上11维超引力的4维和7维形式的几种形式.从4-形式方程出发，我们得到了欧氏AdS_4中与某些边界$Δ_+$ =3算子相匹配的无质量标量和伪标量.事实上，主要的对象是瞬子和畴壁，分别作为外部空间中的完全和部分局部化对象。后者来自于一个（反）M5-膜，它部分地围绕着三个内部方向，类似于模糊S^3/Z_k解。除了第一个解决方案是在原来的M2-膜上增加一些反M2-膜$\mid$（M2-膜）之外，这些对象对几何产生反作用，尽管$\mid$很小（打破所有的超对称性并使真空不稳定）。分别对标量和伪标量采用斜向扰动的8_s $\rightarrow$ 8_v和8_s $\rightarrow$ 8_c得到了对偶三维场论解，而规范场主要用于k= 1，2的情况，即R对称性和超对称性分别增强为SU（4）x U（1）$\rightarrow$ SO（8）和N=6 $\rightarrow$ N=8的情况，以及伪标量的情况.此外，对于赝标量，我们提出了一种特殊的边界变形，它与费米子场等价，这与已经研究过的体m^2=-2共形耦合赝标量的多迹变形是等价的。

英文摘要：

We consider a few ansatzs for the four and seven forms of 11-dimensional supergravity over AdS_4 x S^7/Z_k while try to keep the geometry unchanged. From the 4-form equations, we arrive at some massless scalars and pseudoscalars in the bulk of Euclidean AdS_4 that match with some boundary $Δ_+$=3 operators. Indeed, the main objects are instantons and domain walls as the fully and partially localized objects in the external space, respectively. The latter comes from an (anti)M5-brane wrapping partly around three internal directions similar to the fuzzy S^3/Z_k solutions. Except for the first solutions of adding some anti-M2-branes$\mid$(M2-branes) to the original M2-branes, the objects backreact on the geometry although small$\mid$(break all supersymmetries and destabilize the vacua). The dual 3-dimensional field theory solutions are got by the skew-whiffing 8_s $\rightarrow$ 8_v and 8_s $\rightarrow$ 8_c for the scalars and pseudoscalars respectively, while the gauge fields are used mainly for the k=1,2 cases where the R-symmetry and supersymmetry are enhanced as SU(4) x U(1) $\rightarrow$ SO(8) and N=6 $\rightarrow$ N=8 respectively, and also for pseudoscalars. Further, for the pseudoscalars we propose a special boundary deformation, with a fermion field, that is equivalent to a multi-trace deformation already studied for the bulk m^2=-2 conformally coupled pseudoscalar.

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