幂零李代数轨道上的多黑洞
Multi-black holes from nilpotent Lie algebra orbits
摘要：
对于\ge 2超引力，BPS黑洞解，保持四个超对称性可以线性叠加，导致定义良好的解决方案包含任意数量的这样的BPS黑洞在任意位置。由于是静态的，这些解可以通过在三维空间中耦合到欧几里得引力的伪黎曼空间上的相关非线性西格玛模型来理解。作为本文的主要结果，我们证明了：只要这个伪Riemann空间是不可约对称空间G/H*，这类空间的最一般解都可以完全刻画并由相应的李代数Lie（G）的幂零轨道导出.这种技术也允许显式计算的非超对称极值解，不能通过截断N=2超引力理论。对于极大超引力，我们不仅得到了依赖于32个独立调和函数的BPS解，而且还得到了依赖于29个调和函数的非BPS解。虽然BPS解可以在N=8超引力的适当N=2截断范围内理解，但一般的非BPS解需要理论的全部场内容。
英文摘要：
For N \ge 2 supergravities, BPS black hole solutions preserving four supersymmetries can be superposed linearly, leading to well defined solutions containing an arbitrary number of such BPS black holes at arbitrary positions. Being stationary, these solutions can be understood via associated non-linear sigma models over pseudo-Riemaniann spaces coupled to Euclidean gravity in three spatial dimensions. As the main result of this paper, we show that whenever this pseudo-Riemanniann space is an irreducible symmetric space G/H*, the most general solutions of this type can be entirely characterised and derived from the nilpotent orbits of the associated Lie algebra Lie(G). This technique also permits the explicit computation of non-supersymmetric extremal solutions which cannot be obtained by truncation to N=2 supergravity theories. For maximal supergravity, we not only recover the known BPS solutions depending on 32 independent harmonic functions, but in addition find a set of non-BPS solutions depending on 29 harmonic functions. While the BPS solutions can be understood within the appropriate N=2 truncation of N=8 supergravity, the general non-BPS solutions require the whole field content of the theory.
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