论文标题
BPS表面操作员和校准
BPS surface operators and calibrations
论文作者
论文摘要
我们在这里介绍了6d $ {\ cal n} =（2,0）$理论中BPS表面运算符的全息双重二元研究的仔细研究。最近已经确定了几个不同类别的表面运算符，并且每个类都有特定的校准形式 - $ ads_7 \ times s^4 $中的3型，其回溯到M2-Brane World-volume等于音量形式。除了一个类外，合适的形式外是关闭的，因此M2-Brane的作用很容易以边界数据的形式表达，即表面的几何形状。具体而言，对于消失异常的表面，它与外部曲率平方的积分成正比。通过将两个表面的比率与相同的异常进行比率，可以将其扩展到具有异常情况的情况。在这个理论中，这给出了一系列新的期望值。 对于一类特定的表面运算符，是$ {\ Mathbb r}^4 \ subset {\ Mathbb r}^6 $的Lagrangian submanifolds，该结构要丰富得多，我们发现M2-Branes是一个特殊的Lagrangian Submanifold，它是适当的六维级别的几乎是Calababi-yau submaniford $ ads_的特殊submanifold，ss_ $ ads_7 $ ads_77。这允许对许多这样的例子进行优雅的处理。
We present here a careful study of the holographic duals of BPS surface operators in the 6d ${\cal N}=(2,0)$ theory. Several different classes of surface operators have been recently identified and each class has a specific calibration form - a 3-form in $AdS_7\times S^4$ whose pullback to the M2-brane world-volume is equal to the volume form. In all but one class, the appropriate forms are closed, so the action of the M2-brane is easily expressed in terms of boundary data, which is the geometry of the surface. Specifically, for surfaces of vanishing anomaly, it is proportional to the integral of the square of the extrinsic curvature. This can be extended to the case of surfaces with anomalies, by taking the ratio of two surfaces with the same anomaly. This gives a slew of new expectation values at large $N$ in this theory. For one specific class of surface operators, which are Lagrangian submanifolds of ${\mathbb R}^4\subset {\mathbb R}^6$, the structure is far richer and we find that the M2-branes are special Lagrangian submanifold of an appropriate six-dimensional almost Calabi-Yau submanifold of $AdS_7\times S^4$. This allows for an elegant treatment of many such examples.
