A fixed point formula for the index of multi-centered N = 2 black holes
A fixed point formula for the index of multi-centered N = 2 black holes
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发表时间：
2011
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通讯作者：
J. Manschot;B. Pioline;Ashoke Sen
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作者：
J. Manschot;B. Pioline;Ashoke Sen
我们提出了一个计算多中心解对总BPS指数的（模相关）贡献的公式，该公式表示与单中心解相关的（模无关）指数。我们分析的主要工具是用局域化方法计算N = 2超重力条件下多中心BPS黑洞解的构型自由度的细化指标Tr(−y)3。当中心携带的电荷不允许缩放解（即中心子集可以任意靠近的解）时，经典BPS解的相空间是紧致的，精炼指标定位于旋转下孤立不动点的有限集合，对应于共线解。当电荷允许缩放解时，相空间是非紧致的，但似乎具有有限体积和附加的非孤立不动点的紧致性。我们用“最小修正假设”给出了确定这些固定子流形的贡献的一个公式，并在偶极子晕构型的特殊情况下证明了这一公式。ar X iv:1 10 3。[au:] [au:] [au:] [au：
We propose a formula for computing the (moduli-dependent) contribution of multi-centered solutions to the total BPS index in terms of the (moduli-independent) indices associated to single-centered solutions. The main tool in our analysis is the computation of the refined index Tr (−y)3 of configurational degrees of freedom of multi-centered BPS black hole solutions in N = 2 supergravity by localization methods. When the charges carried by the centers do not allow for scaling solutions (i.e. solutions where a subset of the centers can come arbitrarily close to each other), the phase space of classical BPS solutions is compact and the refined index localizes to a finite set of isolated fixed points under rotations, corresponding to collinear solutions. When the charges allow for scaling solutions, the phase space is non-compact but appears to admit a compactification with finite volume and additional non-isolated fixed points. We give a prescription for determining the contributions of these fixed submanifolds by means of a ‘minimal modification hypothesis’, which we prove in the special case of dipole halo configurations. ar X iv :1 10 3. 18 87 v1 [ he pth ] 9 M ar 2 01 1