四元Kaehler迂回复形与N=2超对称黑洞
Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes
摘要：
研究了由四维N= 2超引力的静态球对称黑洞的径向量子化导出的一类超对称自旋粒子模型。借助c映射，这些自旋粒子在四元数Kaehler流形中运动。它们的旋转自由度描述了迷你超空间缩减的超引力费米子。我们使用BRST迂回复杂技术对这些模型进行了建模。利用局部（世界线）超对称鬼产生特殊的完整变换，构造了一个幂零BRST荷。(An有趣的副产品的建设是一个新的狄拉克运营商的superghost扩展希尔伯特空间。由此产生的量子化模型是规范不变的场论，其场等于特殊四元数矢量丛的截面。它们是巴斯顿发现的Dolbeault上同调的四元数形式的基础和推广。事实上，巴斯顿的情结与我们写下的模型BPS部门有关。我们的研究结果依赖于微积分的四元数凯勒流形上的运营商，从BRST机器，虽然直接由黑洞物理学的动机，可以广泛应用于任何依赖于四元数几何模型。
英文摘要：
We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston's complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kaehler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.
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