本文研究了N=4超杨米尔斯体系中BPS态的超引力跃迁。为了描述这些超引力，我们从IIB超引力的一系列呼吸模约化开始：首先是S^3，然后是S^3 × S^1，最后是S^3 × S^1 × CP^1。然后，我们进行一个完整的超对称性分析，分别得到1/8、1/4和1/2 BPS构型（在最后一步中，我们采用了S^3的霍普夫纤维化）。1/8 BPS几何具有S^3等距性，在六维基底上时间纤维化，通过求解基底上Kahler度规的非线性方程来确定。类似地，1/4 BPS组态有一个S^3 x S^1等距和一个四维基底，其卡勒度规服从另一个非线性的Monge-Ampere型方程。尽管非线性的问题，我们开发了一个通用的起泡AdS描述这些几何形状的边界条件，确保其规律性。在1/8 BPS的情况下，我们发现S^3圈在6维基底内部的5维轨迹上收缩到零大小。要加强完整解的正则性，需要将一个光滑的、通常不连通的五维表面的内部从基底上移除。AdS_5 x S^5基态对应于切除S^5的内部，而1/8 BPS激发对应于S^5的变形（包括拓扑变化）和/或从基底切除额外的液滴。在1/4 BPS构型的情况下，通过强制正则性条件，我们确定了四维基底内部的三维表面，这些表面将S^3收缩到零尺寸的区域与S^1收缩的区域分开。
英文摘要：
This paper focuses on supergravity duals of BPS states in N=4 super Yang-Mills. In order to describe these duals, we begin with a sequence of breathing mode reductions of IIB supergravity: first on S^3, then S^3 x S^1, and finally on S^3 x S^1 x CP^1. We then follow with a complete supersymmetry analysis, yielding 1/8, 1/4 and 1/2 BPS configurations, respectively (where in the last step we take the Hopf fibration of S^3). The 1/8 BPS geometries, which have an S^3 isometry and are time-fibered over a six-dimensional base, are determined by solving a non-linear equation for the Kahler metric on the base. Similarly, the 1/4 BPS configurations have an S^3 x S^1 isometry and a four-dimensional base, whose Kahler metric obeys another non-linear, Monge-Ampere type equation.
Despite the non-linearity of the problem, we develop a universal bubbling AdS description of these geometries by focusing on the boundary conditions which ensure their regularity. In the 1/8 BPS case, we find that the S^3 cycle shrinks to zero size on a five-dimensional locus inside the six-dimensional base. Enforcing regularity of the full solution requires that the interior of a smooth, generally disconnected five-dimensional surface be removed from the base. The AdS_5 x S^5 ground state corresponds to excising the interior of an S^5, while the 1/8 BPS excitations correspond to deformations (including topology change) of the S^5 and/or the excision of additional droplets from the base. In the case of 1/4 BPS configurations, by enforcing regularity conditions, we identify three-dimensional surfaces inside the four-dimensional base which separate the regions where the S^3 shrinks to zero size from those where the S^1 shrinks.
We derive a non-BPS linear ansatz using the charged Weyl formalism in string and M-theory backgrounds. Generic solutions are static and axially-symmetric with an arbitrary number of non-BPS sources corresponding to various brane, momentum and KKm charges. Regular sources are either four-charge non-extremal black holes or smooth non-BPS bubbles. We construct several families such as chains of non-extremal black holes or smooth non-BPS bubbling geometries and study their physics. The smooth horizonless geometries can have the same mass and charges as non-extremal black holes. Furthermore, we fin…
Coarse-graining 1/2 BPS geometries of type IIB supergravity
最近，Lin、Lunin和Maldacena（LLM）（hep-th/0409174）明确地将AdS_5 x S^5上IIB型超引力的1/2 BPS激发映射为自由费米子组态。我们讨论了LLM几何的热粗获得，通过显式映射相应的平衡有限温度费米子配置到超引力。根据马图尔猜想，这类规定应该在几何中产生一个视界。在有限温度平衡LLM几何中，我们没有发现视界。这很可能是由于粗粒化只在IIB型超引力的完整希尔伯特空间的半BPS扇区中进行。对于远小于AdS曲率尺度的温度，发现对应于近简并对偶费米气体的平衡背景解析。
We build the first family of smooth bubbling microstate geometries that are asymptotic to the near-horizon region of extremal five-dimensional Kerr black holes (NHEK). These black holes arise as extremal non-supersymmetric highly-rotating D1-D5-P solutions in type IIB string theory on T$^4\times$S$^1$. Our solutions are asymptotically NHEK in the UV and end in the IR with a smooth cap. In the context of the Kerr/CFT correspondence, these bubbling geometries are dual to pure states of the 1+1 dimensional chiral conformal field theory dual to NHEK. Since our solutions have a bubbling structure i…
We construct large classes of non-BPS smooth horizonless geometries that are asymptotic to AdS$_3\times$S$^3\times$T$^4$ in type IIB supergravity. These geometries are supported by electromagnetic flux corresponding to D1-D5 charges. We show that Einstein equations for systems with eight commuting Killing vectors decompose into a set of Ernst equations, thereby admitting an integrable structure. This feature, which can a priori be applied to other AdS$_D\times\mathcal{C}$ settings in supergravity, allows us to use solution-generating techniques associated with the Ernst formalism. We explicitl…
We investigate half-BPS Type IIB supergravity solutions with spacetime geometry $AdS_2\times S^6$ warped over a Riemann surface $Σ$. The general local solution was obtained in earlier work in terms of two holomorphic functions $\mathcal A_\pm$ on $Σ$. In the first part of this paper we seek global solutions corresponding to the near-horizon behavior of $(p,q)$-string junctions. We identify the type of singularity in $\mathcal A_\pm$ needed at the boundary of $Σ$ to match the solutions locally onto the classic $(p,q)$-string solution. We construct solutions with multiple $(p,q)$-strings, but th…
Non-BPS D-brane Solutions in Six Dimensional Orbifolds
从Eyras和Panda最近构造的IIB/ $(-1)^{F_L}I_4$的非BPS D 0-膜解出发，利用T-对偶构造了Sen预言的IIB/ $(-1)^{F_L}I_4$和IIA/ $(-1)^{F_L}I_4$的非BPS D 2-膜和D 1-膜解。而D1-膜耦合（电和磁）到NS 5A-膜的自对偶2-形式的潜力，这是目前在IIA型orbifold结构的扭曲部门。最后，我们讨论了这些膜的11维解释，起源于一个非BPS的M-理论定向折叠的$Ω_ρI_5$的M1-膜的解决方案。
To study the quantized Coulomb branch of 3d $\mathcal{N}=4$ unitary SQCD theories, we propose a new method to compute correlators of monopole and Casimir operators that are inserted in the $\mathbb{R}\times\mathbb{R}^2_ε$ Omega background. This method combines results from supersymmetric localization with inputs from the brane realisation of the correlators in type IIB string theory. The main challenge is the computation of the partition functions of certain Super-Matrix-Models (SMMs), which appear in the contribution of monopole bubbling sectors and are realised as the theory living on the D1…
我们构造了描述AdS_2 x S^2的归一化激发的BPS几何。所有正则无视界解都由R^3中的两个调和函数参数化，源沿闭合曲线。这种局部结构让人想起了其他AdS情形的“冒泡解”，然而，由于AdS_2的特殊渐近性质，R^3的一个副本并不能覆盖整个空间，我们讨论了解析延拓的过程，这导致了新几何的非平凡拓扑结构。我们还研究了新几何上的超对称膜探针，它们代表了巨引力子的AdS_2 × S^2对应物。
We construct the first smooth bubbling geometries using the Weyl formalism. The solutions are obtained from Einstein theory coupled to a two-form gauge field in six dimensions with two compact directions. We classify the charged Weyl solutions in this framework. Smooth solutions consist of a chain of Kaluza-Klein bubbles that can be neutral or wrapped by electromagnetic fluxes, and are free of curvature and conical singularities. We discuss how such topological structures are prevented from gravitational collapse without struts. When embedded in type IIB, the class of solutions describes D1-D5…
