二重子算符的几何性质
Geometric aspects of dibaryon operators
摘要：
N = 1的超共形场论的AdS/CFT对应表明，二重子算符与AdS中的点状D膜态是对偶的，并且在Sasaki-Einstein流形中包裹着各种循环。它还表明，D-膜的体积给出了相应算子的R-荷。我们阐明这一对应关系的各个方面，特别注意研究的情况下，膜的尖端三个不同的卡拉比丘锥。我们证明了描述共形场论的图中的箭头可以被认为是Calabi-Yau几何上的非平凡全纯向量丛的整体截面。我们认为，这些截面的零轨迹给出了几何映射，使我们能够将一个特定的二重子与一个全纯循环联系起来，通过在离原点固定距离处将相应的循环与Sasaki-Einstein轨迹相交。我们表明，这可以与相应的体积的佐佐木-爱因斯坦空间，一个得到确切的协议之间的体积的周期确定与此程序和R-收费的运营商。
英文摘要：
The AdS/CFT correspondence for N=1 Super conformal field theories suggests that dibaryon operators are dual to D-brane states that are point like in AdS and that wrap various cycles in a Sasaki-Einstein manifold. It also suggests that the volume of the D-brane gives the R-charge of the corresponding operator. We elucidate various aspects of this correspondence, paying particular care to study the case of branes at the tip of three different Calabi Yau cones. We show that the arrows in the quiver diagram describing the conformal field theory can be thought of as global sections of a non-trivial holomorphic vector bundle over the Calabi-Yau geometry. We suggest that the zero locus of these sections gives the geometric map that lets us tie a particular dibaryon to a holomorphic cycle, by intersecting the corresponding cycle with the Sasaki-Einstein locus at fixed distance from the origin. We show that this can be compared with the corresponding volumes of the Sasaki-Einstein space and that one gets exact agreement between the volumes of the cycles identified with this procedure and the R-charges of the operators.
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