论文标题
广告黑洞和有限n个指数
AdS black holes and finite N indices
论文作者
论文摘要
我们研究4D $ \ MATHCAL {N} = 4 $ YANG-MILLS理论的索引，并使用$ u（n）$ gauge组，重点关注$ ads_5 \ times s^5 $的双BPS黑洞的物理。这些黑洞的某些方面可以从有限的$ n $ indices中研究，并具有相当大的$ n^2 $。我们通过将其扩展到散发性的高订单，对$ n \ leq 6 $的指数进行数值研究。该指数的熵与双黑洞的Bekenstein-Hawking熵非常吻合，例如$ n^2 = 25 $或$ 36 $。我们的数据阐明并支持了最近的思想，这些想法允许从指数中对这些黑洞进行分析研究，例如Legendre转换的复杂鞍点和索引中的振荡标志。特别是，复杂的鞍点自然解释了$ \ frac {1} {n} $ - 索引的振荡模式。我们还通过研究Macmahon函数倒数的模型来说明我们思想的普遍性。
We study the index of 4d $\mathcal{N}=4$ Yang-Mills theory with $U(N)$ gauge group, focussing on the physics of the dual BPS black holes in $AdS_5\times S^5$. Certain aspects of these black holes can be studied from finite $N$ indices with reasonably large $N^2$. We make numerical studies of the index for $N\leq 6$, by expanding it up to reasonably high orders in the fugacity. The entropy of the index agrees very well with the Bekenstein-Hawking entropy of the dual black holes, say at $N^2=25$ or $36$. Our data clarifies and supports the recent ideas which allowed analytic studies of these black holes from the index, such as the complex saddle points of the Legendre transformation and the oscillating signs in the index. In particular, the complex saddle points naturally explain the $\frac{1}{N}$-subleading oscillating patterns of the index. We also illustrate the universality of our ideas by studying a model given by the inverse of the MacMahon function.
