AI 中文总结
研究AdS₂/CFT₁全息中极端超对称黑洞微观描述问题，通过局域化技术推导超共形箭图指标的不动点公式，以循环阿贝尔箭图为例，在大 N 极限下精确捕捉微观标度BPS指标贡献，为AdS₂/CFT₁对偶弦论实现助力。
AI 中文摘要
尽管在近极端黑洞物理的统计描述方面有了进展，但 AdS₂/CFT₁全息中极端超对称黑洞的微观描述仍不清楚。本文重新审视了Denef对库仑分支中D膜束缚态的箭图力学描述，其在AdS₂标度极限下展现出一种涌现的共形对称性，但在库仑分支和希格斯分支相交处附近会因超势修正而被打破。为阐明此问题，我们用局域化技术推导并解释了超共形箭图指标的不动点公式。以循环阿贝尔箭图为例，在特定大 N 极限下，不动点位于共形描述可靠的区域。在此极限下，我们对超共形指标的表达式精确捕捉到了Beaujard、Mondal和Pioline推导的微观标度BPS指标的一个贡献，此前在库仑分支上不可见。我们的结果有望为AdS₂/CFT₁对偶的弦论实现迈出一步。
英文摘要
The microscopic description of extremal supersymmetric black holes in AdS$_2$/CFT$_1$ holography has remained elusive despite recent progress in the statistical description of near-extremal black hole physics. In this work we revisit Denef's quiver mechanics description of D-brane bound states in the Coulomb branch, which displays an emergent conformal symmetry in the AdS$_2$ scaling limit. This conformal symmetry is however broken by superpotential corrections near the locus where the Coulomb and Higgs branches meet, and its significance has so far remained unclear. In order to to clarify this issue, we derive and interpret a fixed-point formula for the superconformal quiver index using localization techniques. Focusing on cyclic abelian quivers, we show that, in a certain large-$N$ limit (with the rank $N$ of the quiver gauge group), the fixed points are located in the regime where the conformal description is reliable. In this limit, our expression for the superconformal index precisely captures a contribution to the microscopic scaling BPS index derived by Beaujard, Mondal and Pioline, which was hitherto not visible on the Coulomb branch. Our results are hoped to provide a step towards a stringy realization of AdS$_2$/CFT$_1$ duality.
Comments35 pages, 1 figure
