论文标题
从重力路径积分计数的黑洞微晶
Black hole microstate counting from the gravitational path integral
论文作者
论文摘要
从重力路径积分中重现黑洞微型群体的整数计数是量子重力的重要问题。在本文中，我们表明，通过使用超对称性定位，$ \ frac {1} 8 $ -bps黑洞的重力路径积分不可或缺，以$ \ MATHCAL {N} = 8 $ SuperGravity重现了在此类黑洞的弦乐理论构建中获得的索引，包括所有非固定式地球抑制。然后，一个更精致的论点表明，不仅是黑洞指数，而且还表明，在电荷中多项式抑制的能量窗口内的黑洞微晶格总数也与该字符串理论索引相匹配。 为了实现这样的匹配，我们计算了所有$ \ MATHCAL {n} = 2 $ supergravity Supermultiplets在$ \ MATHCAL {N} = 8 $ GRAVITY SUPERMULTIPLET中产生的本地化计算中产生的单循环决定因素。此外，我们仔细说明了边界零模型的贡献，这可以看作是由于$ \ Mathcal {n} = 4 $ super-Schwarzian的零温度极限引起的，并表明在此类模式上执行精确的路径积分提供了对比赛的关键贡献。同伴论文中介绍了关于所有极端黑洞的更广泛背景下这种零模型的重要性的讨论。
Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In this paper, we show that, by using supersymmetric localization, the gravitational path integral for $\frac{1}8$-BPS black holes in $\mathcal{N}=8$ supergravity reproduces the index obtained in the string theory construction of such black holes, including all non-perturbatively suppressed geometries. A more refined argument then shows that, not only the black hole index, but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges, also matches this string theory index. To achieve such a match we compute the one-loop determinant arising in the localization calculation for all $\mathcal{N}=2$ supergravity supermultiplets in the $\mathcal{N}=8$ gravity supermultiplet. Furthermore, we carefully account for the contribution of boundary zero-modes, that can be seen as arising from the zero-temperature limit of the $\mathcal{N}=4$ super-Schwarzian, and show that performing the exact path integral over such modes provides a critical contribution needed for the match to be achieved. A discussion about the importance of such zero-modes in the wider context of all extremal black holes is presented in a companion paper.
