AI 中文总结
该研究构造五维引力超对称指标的一般鞍点并提升到IIB超引力，分析双中心鞍点性质，匹配其壳上作用量与椭圆亏格的Farey尾展开，确认部分解不对D1-D5椭圆亏格贡献。
AI 中文摘要
我们首先构造了具有$S^1\times\boldsymbol{\rm R}^4$渐近行为的五维引力超对称指标的一般鞍点，其携带任意数量的电荷以及Gibbons-Hawking中心。随后我们将三电荷构型提升到IIB型超引力中，得到渐近于$S^1\times\boldsymbol{\rm R}^4\times S^1\times {\rm K}3$的解，其携带D1-D5-P电荷。在取解耦极限时，这些解产生渐近于欧几里得AdS$_3\times S^3\times {\rm K}3$的候选鞍点，对应对偶CFT$_2$的椭圆亏格。我们重点关注双中心鞍点，其包含三个指定orbifold作用的整数。根据这些整数，鞍点可能具有或不具有欧几里得视界，且可能是光滑的或表现出orbifold奇点。我们在适当的系综中给出这些双中心鞍点的壳上作用量，并建立其与椭圆亏格的Farey尾展开的精确匹配。无视界鞍点是文献中先前讨论的分数谱流解的欧几里得版本，对应$({\rm AdS}_3\times S^3)/\boldsymbol{\rm Z}_k$ orbifold。黑洞鞍点是无视界鞍点的模像，它们通过将其置于$\boldsymbol{\rm Z}_k$ orbifold背景中推广了熟知的${\rm SL}(2,\boldsymbol{\rm Z})$族的BTZ黑洞。我们还考虑了五维黑环和黑透镜鞍点的解耦极限产生的渐近AdS$_3\times S^3$解，给出其壳上作用量并确认它们不对D1-D5椭圆亏格产生贡献。
英文摘要
We first construct general saddles of the five-dimensional gravitational supersymmetric index with $S^1\times\mathbb{R}^4$ asymptotics, carrying an arbitrary number of electric charges and Gibbons-Hawking centers. We then uplift the three-charge configurations to type IIB supergravity, obtaining solutions asymptotic to $S^1\times \mathbb{R}^4\times S^1\times {\rm K}3$, carrying D1-D5-P charges. Upon taking a decoupling limit, these solutions yield asymptotically Euclidean AdS$_3\times S^3\times {\rm K}3$ candidate saddles of the dual CFT$_2$ elliptic genus. We focus on the two-center saddles, which involve three integers specifying an orbifold action. Depending on these integers, the saddles may or may not possess a Euclidean horizon, and may be smooth or exhibit orbifold singularities. We give the on-shell action of these two-center saddles in the appropriate ensemble and establish a precise match with the Farey-tail expansion of the elliptic genus. The horizonless saddles are the Euclidean version of fractional spectral-flow solutions previously discussed in the literature, corresponding to $({\rm AdS}_3\times S^3)/\mathbb{Z}_k$ orbifolds. The black hole saddles are modular images of the horizonless ones. They generalize the well-known ${\rm SL}(2,\mathbb{Z})$ family of BTZ black holes by placing it in the background of the $\mathbb{Z}_k$ orbifold. We also consider the asymptotically AdS$_3\times S^3$ solutions arising as decoupling limit of five-dimensional black ring and black lens saddles, provide their on-shell action and confirm that they do not contribute to the D1-D5 elliptic genus.
Comments53 pages
