arXiv 1303.26342013-03-11hep-th

动力学破缺超对称的引力对偶

Gravity dual of dynamically broken supersymmetry

William Cottrell, Jerome Gaillard, Akikazu Hashimoto

备注：: 38 pages, 6 figures
DOI：: 10.1007/JHEP08(2013)105

摘要：

我们研究了嵌入到翘曲A_8几何中的ABJM理论的重整化群流，并探讨了真空结构对理论参数的依赖性。该模型具有积群规范结构U（N）xU（n+1），并配备了离散参数N、l和k，与两个规范群的杨-米尔斯耦合比相关的连续参数b，以及设定总尺度的一维参数gYM^2。当Q=N-l（l-k）/2k-k/24为正时，超对称超引力解存在，并且可以解释为从类杨-米尔斯UV不动点到超共形IR不动点的RG流，自由能为Q^3/2阶。当Q取为负值时，理论的命运就不那么清楚了。我们通过考虑在Q=0的背景上添加少量反膜的线性化引力反作用，探索了小负Q的可能引力解的结构。继Bena等人的工作之后，我们发现满足适当边界条件的合理解似乎不存在。这使得Q<0理论的RG流的状态成为一个谜。我们对这个难题提出了以下推测性的解决方案：由曲率修正引起的超引力-k/24单位的电荷应该被认为是一个允许的物理对象，人们应该在Q=-k/24的背景上而不是在Q=0的背景上增加一个反膜。这样的解有一个排斥奇点，并给出了真空构型的图像，其中一簇反膜漂浮在排斥奇点周围，但被其他通量稳定下来，不会被推到无穷远。这样的状态是非超对称的，并且似乎描述了具有超对称性动力学破缺的真空。基于这些考虑，我们构建了一个相图，这个理论展示了各种有趣的区域。

英文摘要：

We study a renormalization group flow of ABJM theory embedded into the warped A_8 geometry and explore the dependence of the vacuum structure on the parameters of the theory. This model has a product group gauge structure U(N)xU(n+l) and comes equipped with discrete parameters N, l and k, a continuous parameter b related to the ratio of the Yang-Mills coupling for the two gauge groups, and one dimensionful parameter gYM^2 setting the overall scale. A supersymmetric supergravity solution exists when Q=N-l(l-k)/2k-k/24 is positive and is interpretable as a RG flow from a Yang-Mills like UV fixed point to a superconformal IR fixed point with free energy of order Q^3/2. The fate of the theory when Q is taken to be negative is less clear. We explore the structure of the possible gravity solution for small negative Q by considering the linearized gravitational back reaction from adding a small number of anti-branes on the Q=0 background. Following the work of Bena, et.al., we find that a sensible solution satisfying appropriate boundary conditions does not appear to exist. This leaves the status of the RG flow for the Q<0 theories a mystery. We offer the following speculative resolution to the puzzle: the -k/24 unit of charge induced by the curvature correction to supergravity should be considered an allowed physical object, and one should be adding an anti brane not to the Q=0 background but rather the Q=-k/24 background. Such a solution has a repulson singularity, and gives rise to a picture of the vacuum configuration where a cluster of anti-branes are floating around the repulson singularity, but are stabilized from being pushed off to infinity by other fluxes. Such a state is non-supersymmetric and appears to describe a vacuum with dynamical breaking of supersymmetry. Based on these considerations, we construct a phase diagram for this theory exhibiting various interesting regions.

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英文摘要：

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