D1-D5-P 黑弦的引力指数
Gravitational index of the D1-D5-P black string
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中文总结 AI 辅助
研究 D1-D5-P 黑弦的引力指数，通过给出欧几里得引力路径积分的鞍点，利用十维 IIB 超引力理论的复超对称非极端解，经一系列操作，最终得到相关解并重现对偶理论的卡迪公式。
中文摘要 AI 辅助
我们给出了与 D1-D5-P 黑弦的超对称指数相对应的欧几里得引力路径积分（GPI）的鞍点。这些鞍点是十维 IIB 超引力理论具有任意逆温度β的复的、超对称的、非极端解。解带有固定的单极荷\(Q_1\)、\(Q_5\)、\(Q_n\)和与极端超对称黑弦相等的角动量\(J_L\)。关键的是，解有固定角速度\(\Omega_{R} = - 2 \pi i /\beta\)，它是与\(J_R\)对偶的化学势。这实现了在 GPI 中插入\((-1)^{F}\)。吉本斯 - 霍金运动时作用量与温度无关且与具有相同单极荷的极端黑弦的超对称指数一致。在取有限温度近视界解耦极限后，我们得到\(S^3\)纤维化在 BTZ 上的解。虽然这些近视界解有有限全纯和反全纯模参数，但其运动时作用量重现了对偶 D1-D5 SCFT₂的全纯椭圆亏格的卡迪公式。
英文摘要
We present saddle-points of the Euclidean Gravitational Path Integral (GPI) corresponding to the supersymmetric index of the D1-D5-P black string. These saddles are complex, supersymmetric, non-extremal solutions of 10-dimensional IIB supergravity theory with arbitrary inverse temperature $β$. The solutions carry fixed monopole charges $Q_1$, $Q_5$, $Q_n$, and angular momentum $J_L$ equal to the extremal supersymmetric black string. Crucially, the solutions have fixed angular velocity $Ω_{R} = - 2 πi /β$, which is the chemical potential dual to $J_R$. This implements the insertion of $(-1)^{F}$ in the GPI. The Gibbons-Hawking on-shell action is temperature-independent and agrees with the supersymmetric index of the extremal black string carrying the same monopole charges. Upon taking a finite-temperature near-horizon decoupling limit, we obtain solutions of the form $S^3$ fibered over BTZ. Although these near-horizon solutions have finite holomorphic and anti-holomorphic modular parameters, their on-shell action reproduces the Cardy formula of the holomorphic elliptic genus of the dual D1-D5 SCFT$_2$.
