AI 中文总结
研究反德西特黑洞鞍点对d维共形场论谱形式因子的贡献，通过分析高温下大黑洞引力作用及相关行为，利用皮卡 - 勒夫谢茨分析揭示斯托克斯现象，得出不同维度下黑洞鞍点主导地位变化及对谱形式因子斜率影响的结论。
AI 中文摘要
我们分析了反德西特黑洞鞍点对具有引力对偶的d维共形场论谱形式因子的贡献。在高温下，大反德西特黑洞的解析延拓引力作用有望给出谱形式因子‘斜率’的主导大N近似。当共形场论置于半径为\(\ell\)的(d - 1)维空间球面上时，我们表明对于\(d\equiv5\,({\rm mod}\; 4)\)，这种评估意味着在\(t\gg \ell\)时\(Z(\beta +it)\)的非物理行为。对\(Z(\beta+it)\)的一个迷你超空间近似的皮卡 - 勒夫谢茨分析确实揭示了恢复一致性所需的斯托克斯现象。发现对于\(d>3\)，大反德西特黑洞鞍点失去主导地位，并随后在\(t = O(\beta)\)时与相关积分回路断开连接。对于\(d = 3\)，主导地位在\(\beta\)量级的时间失去，而斯托克斯断开发生在\(t = O(\ell)\)。在大黑洞鞍点与路径积分轮廓断开连接后，谱形式因子的斜率由谱的低能端主导。
英文摘要
We analyze the contribution of AdS black hole saddles to the spectral form factor of $d$-dimensional CFTs with a gravity dual. At high temperatures, the analytically continued gravitational action of the large AdS black hole is expected to give a leading large-$N$ approximation to the 'slope' of the spectral form factor. When the CFT is put on a $(d-1)$-dimensional spatial sphere of radius $\ell$, we show that such an evaluation implies unphysical behavior of $Z(β+it)$ at large $t\gg \ell$ for $d\equiv5 \,({\rm mod}\; 4)$. A Picard--Lefschetz analysis of a minisuperspace approximation to $Z(β+it) $ does reveal the required Stokes phenomena that restore consistency. It is found that for $d>3$, the large AdS black hole saddle loses dominance and subsequently disconnects from the relevant integration cycle at $t=O(β)$. For $d=3$, dominance is lost at a time of order $β$, while the Stokes disconnection takes place at $t=O(\ell)$. After the large black hole saddle disconnects from the path-integral contour, the slope of the spectral form factor becomes dominated by the low-energy end of the spectrum.
Comments21 pages, 6 figures. Two references added
