论文标题
渐近广告指标上的谐波形式
Harmonic forms on asymptotically AdS metrics
论文作者
论文摘要
在本文中，我们研究了爱因斯坦指标$ g $的2-参数家族的旋转不变的谐波共同体，该家族接受了$ su（2）\ times u（1）$的共同均匀性，并且具有广告渐近性。根据参数的值，如果$ u（1）$ action的固定点基因座是0维，则是螺栓类型，如果是二维，则$ g $是螺母类型的。我们发现，如果$ g $是螺母类型，那么$ su（2）$ invariant谐波2形式的空间是3维的，完全由自动划分形式组成；如果$ g $是螺栓类型，则为4维。在这两种情况下，我们都明确确定一个基础。对$ f $ a自动辅助2形式的$ $（g，f）$也是玻色粒领域的解决方案，$ 4D $ supergravity。我们确定哪种选择是超对称溶液和保留的超对称性的量。
In this paper we study the rotationally invariant harmonic cohomology of a 2-parameter family of Einstein metrics $g$ which admits a cohomogeneity one action of $SU (2) \times U (1) $ and has AdS asymptotics. Depending on the values of the parameters, $g$ is either of NUT type, if the fixed-point locus of the $U (1) $ action is 0-dimensional, or of bolt type, if it is 2-dimensional. We find that if $g$ is of NUT type then the space of $SU (2) $-invariant harmonic 2-forms is 3-dimensional and consists entirely of self-dual forms; if $g$ is of bolt type it is 4-dimensional. In both cases we explicitly determine a basis. The pair $(g,F)$ for $F$ a self-dual harmonic 2-form is also a solution of the bosonic sector of $4D $ supergravity. We determine for which choices it is a supersymmetric solution and the amount of preserved supersymmetry.
