论文标题
带有许多Rarita-Schwinger田地的歧管
Manifolds with many Rarita-Schwinger fields
论文作者
论文摘要
Rarita-Schwinger操作员是仅限于3/2型机器的扭曲的Dirac操作员。 Rarita-Schwinger字段是该操作员的解决方案，这些解决方案不含差异。这是一个过度确定的问题，解决方案很少见。有大量的解决方案空间更加出乎意料。在本文中，我们证明了在任何给定维度上的紧凑型歧管序列的存在，大于或等于4，而Rarita-Schinginger田地的空间尺寸倾向于无穷大。这些歧管要么简单地将Kähler-Einstein自旋与负爱因斯坦常数连接起来，要么是具有平坦托里的空间的产物。此外，我们构建了比较复杂维度的calabi-yau歧管，比相同尺寸的扁平托里，具有更线性独立的rarita-schwinger场。
The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kähler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
