arXiv 1406.51292014-06hep-th

东方褶皱的精确探针

Exact probes of orientifolds

Bartomeu Fiol, Blai Garolera, Genis Torrents

备注：: 28 pages. v2: Added references
DOI：: 10.1007/JHEP09(2014)169

摘要：

本文用$G=SO(N),Sp(N)$计算了欧氏${\cal N}=4$超杨-米尔斯在基本表象和旋量表象下的圆威尔逊圈的真空期望值.这些场论与在$AdS_5\times {\mathbb R} {\mathbb P}^5$上紧化的IIB型弦论是对偶的，加上某些离散挠率的选择，我们用我们的结果来探测这种全息对偶。我们首先回顾了具有$AdS_5\times {\mathbb R} {\mathbb P}^5$作为基态的LLM型几何结构。我们的研究结果澄清和完善这些LLM型几何形状的识别所产生的半谐振子上的费米子冒泡的几何形状。我们还确定了存在的离散扭转与一费米子维格纳分布成为负的相空间的起源。然后，我们转向弦世界片解释我们的结果，并认为，对于所考虑的数量，它们意味着两个特点：第一，来自世界片的贡献与一个单一的crossscap是密切相关的贡献来自定向世界片，第二，世界片有两个crossscap不有助于这些数量。

英文摘要：

We compute the exact vacuum expectation value of circular Wilson loops for Euclidean ${\cal N}=4$ super Yang-Mills with $G=SO(N),Sp(N)$, in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on $AdS_5\times {\mathbb R} {\mathbb P}^5$ plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having $AdS_5\times {\mathbb R} {\mathbb P}^5$ as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely related to the contribution coming from orientable world-sheets, and second, world-sheets with two crosscaps don't contribute to these quantities.

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