Cariglia Marco, Mac Conamhna Oisín A P
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Phys Rev Lett. 2005 Apr 29;94(16):161601. doi: 10.1103/PhysRevLett.94.161601. Epub 2005 Apr 28.
We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of 11-dimensional supergravity. The metric, four-form, and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four-form field equation to ensure that the solution of the Killing spinor equation also satisfies all the field equations, and we give these conditions explicitly.
对于允许具有Spin(7)结构的时空，我们推导了11维超引力的Killing旋量方程的一般局部玻色子解。度规、四形式场以及Killing旋量都被明确确定，直到一个具有Spin(7)全纯性的任意八维流形。施加比安基恒等式和四形式场方程的一个特定分量就足以确保Killing旋量方程的解也满足所有场方程，并且我们明确给出了这些条件。
