我们提出了一个一致的截断的IIB超引力流形承认一个Sasaki-Einstein结构，它保持了度量和五个真正的标量场。这个理论可以进一步截断为一个约束的单参数族，它只依赖于度量和一个标量，以及一个度量和三个标量的理论。约化理论允许超对称和非超对称的AdS_5和AdS_4 x R解。我们分析了AdS临界点周围的频谱，并确定了对偶算子。
英文摘要：
We present a consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, which keeps the metric and five real scalar fields. This theory can be further truncated to a constrained one-parameter family that depends on only the metric and one scalar, as well as to a theory with a metric and three scalars. The reduced theory admits supersymmetric and non-supersymmetric AdS_5 and AdS_4 x R solutions. We analyze the spectrum around the AdS critical points and identify the dual operators.
We study generalised calibrations described by Exceptional Sasaki-Einstein structures on AdS backgrounds in type IIB and M-theory, placing the focus on the generalised Reeb vectors. The inequalities for the energy bound are derived by decomposing a $κ$-symmetry condition and equivalently, bispinors in calibration conditions from existing literature. We explain how the closure of the calibration forms is related to the integrability conditions of the Exceptional Sasaki-Einstein structure, in particular for AdS space-filling or point-like branes. Doing so, we show that the form parts of the twis…
We show that for every Sasaki-Einstein manifold, $M_5$, the AdS$_5\times M_5$ background of type IIB supergravity admits two universal deformations leading to supersymmetric AdS$_4$ solutions. One class of solutions describes an AdS$_4$ domain wall in AdS$_5$ and is dual to a Janus configuration with $\mathcal{N}=1$ supersymmetry. The other class of backgrounds is of the form AdS$_4\times S^1\times M_5$ with a non-trivial SL$(2,\mathbb{Z})$ monodromy for the IIB axio-dilaton along the $S^1$. These AdS$_4$ solutions are dual to three-dimensional $\mathcal{N}=1$ SCFTs. Using holography we expres…
We study holographic dual descriptions of very special conformal field theories with the T(2) symmetry. After constructing solutions in effective five dimensional Einstein gravity coupled with massive two-form fields, we uplift them to the ten dimensional type IIB supergravity, via a consistent truncation ansatz, to derive new analytical solutions in string theory. From the Kaluza-Klein ansatz in terms of the internal Sasaki-Einstein space, we obtain their field theory interpretation with concrete realizations in a large class of holographic $\mathcal{N}=1$ supersymmetric conformal field theor…
We study maximally supersymmetric Anti-de Sitter backgrounds in consistent N=2 truncations of type IIB supergravity compactified on the Sasaki-Einstein manifold $T^{1,1}$. In particular, we focus on truncations that contain fields coming from the nontrivial second and third cohomology forms on $T^{1,1}$. These give rise to N=2 supergravity coupled to two vector- and two hypermultiplets (Betti-vector truncation) or one vector- and three hypermultiplets (Betti-hyper truncation), respectively. We find that both truncations admit AdS$_5$ backgrounds with the gauge group always being broken but con…
We show that for every positive curvature Kahler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X_{2n+3} in dimension 2n+3. When n=1 we recover a recently discovered family of supersymmetric AdS_5 x X_5 solutions of type IIB string theory, while when n=2 we obtain new supersymmetric AdS_4 x X_7 solutions of D=11 supergravity. Both are expected to provide new supergravity duals of superconformal field theories.
We investigate compactifications of type II and M-theory down to $AdS_5$ with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry. The geometric data and gauge fields on the internal manifold are encoded in a pair of generalized structures corresponding to the vector and hyper-multiplets of the reduced five-dimensional supergravity. Supersymmetry translates into integrability conditions for these structures, generalizing, in the case of type IIB, the Sasaki-Einstein conditions. We show that the ten and eleven-dimensional type IIB and M-theory K…
We consider the most general AdS$_3$ solutions of type IIB supergravity admitting a dynamical SU$(3)$ structure and preserving $\mathcal{N}=(0,2)$ supersymmetry. The analysis is broken into three distinct classes depending on whether the dynamical SU$(3)$ structure degenerates to a strict SU$(3)$ structure. The first class we consider allows for a holomorphically varying axio-dilaton consistent with the presence of $(p,q)$ 7-branes in addition to D3-branes and $(p,q)$ 5-branes. In the remaining two classes the axio-dilaton may vary but does not do so holomorphically. The second class of soluti…
We show how to expand the Lunin-Maldacena solution to the full bosonic sector of gauged $\mathcal N=2$ supergravity. In particular, we construct a consistent truncation of IIB supergravity on a $β$-deformed $\mathrm{AdS}_5\times S^5$ background retaining a dynamical metric and graviphoton in five dimensions. We comment on the relation between this solution and similar constructions on Sasaki-Einstein manifolds, as well as the possibility of further consistent truncations which generalize the Lunin-Maldacena solution.
We discuss in detail the different analogues of Dolbeault cohomology groups on Sasaki-Einstein manifolds and prove a new vanishing result for the transverse Dolbeault cohomology groups $H_{\bar\partial}^{(p,0)}(k)$ graded by their charge under the Reeb vector. We then introduce a new cohomology, $η$-cohomology, which is defined by a CR structure and a holomorphic function $f$ with non-vanishing $η\equiv \mathrm{d}f$. It is the natural cohomology associated to a class of supersymmetric type IIB flux backgrounds that generalise the notion of a Sasaki-Einstein manifold. These geometries are dual …
在一般的假设下，我们表明，在d+1维的引力理论承认AdS解决方案可以减少到d维理论包含Lifshitz解决方案与动力学指数z=2。在d=4，N=2的超引力系统中，我们证明了如果AdS背景是N=2超对称的，则Lifshitz几何保持1/4的超荷，并构造了相应的Killing旋量.我们说明这些结果的例子从超对称一致截断的IIB型超引力，提高类已知的4维Lifshitz解决方案的弦论。作为副产品，我们发现了一个新的AdS 4 x S1 x T（1，1）的IIB型解决方案。
We construct supersymmetric $AdS_3\times Σ$ solutions of minimal gauged supergravity in $D=5$, where $Σ$ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on $S^5$, or more generally on any regular Sasaki-Einstein manifold, to smooth solutions of type IIB supergravity. The solutions are dual to $d=2$, $\mathcal{N}=(0,2)$ SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on $Σ$. Unlike for smooth $Σ$ the superconformal R-symmetry mixes with the $U(1)$ isometry of the spindle.
We analyse generic AdS flux backgrounds preserving eight supercharges in $D=4$ and $D=5$ dimensions using exceptional generalised geometry. We show that they are described by a pair of globally defined, generalised structures, identical to those that appear for flat flux backgrounds but with different integrability conditions. We give a number of explicit examples of such "exceptional Sasaki-Einstein" backgrounds in type IIB supergravity and M-theory. In particular, we give the complete analysis of the generic AdS$_5$ M-theory backgrounds. We also briefly discuss the structure of the moduli sp…
Membranes with Topological Charge and AdS4/CFT3 Correspondence
如果Sasaki-Einstein流形Y ^7的第二贝蒂数b_2不为零，则AdS_4 x Y ^7上的M理论具有“拓扑”U（1）^{b_2}规范对称性。相应的阿贝尔规范场来自三种形式的涨落，其中一种在AdS_4中，另外两种在Y ^[7]中。我们发现黑膜溶液带有这些U（1）电荷之一。在零温度极限下，我们的解在紫外线的AdS_4 x Y^7和红外线的AdS_2 x R^2 x压缩Y^7之间插值。事实上，AdS_2 x R^2 x压缩Y^7背景本身就是超引力运动方程的解。这些解似乎并不保持任何超对称性。我们搜索它们可能的不稳定性，但没有发现任何不稳定性。我们还讨论了在具有整体U（1）电荷密度的双Chern-Simons规范理论中带电膜背景的意义。最后，我们提出了一个简单的解析解，它具有相同的红外，但不同的紫外行为。我们把这个解归结为IIA型弦论，并把T-对偶化为IIB型。IIB型度规是被压缩的Y ^[7]和极值BTZ黑洞的乘积。我们讨论了在部分包裹在压缩Y上的D3-膜上的（1+1）维CFT对这种IIB型背景的解释^[7]。
Symmetry-breaking vacua and baryon condensates in AdS/CFT
本文研究了AdS_5 x Y上超共形场论、与IIB型弦论对偶的AdS/CFT的引力破缺形变，其中Y是Sasaki-Einstein流形.在这些真空中，共形不变性和重子对称性都自发破缺。我们提出了一个详细的讨论超引力模空间，其中涉及平坦形式的渐近锥卡-丘流形上的字段，并匹配到规范理论真空模空间。我们讨论了某些线性波动的模量，确定戈德斯通玻色子与非异常重子对称性的自发破缺。其余的模场与反常重子对称性的自发破缺有关。我们还详细说明的建议，计算重子算子的凝聚相当于计算的配分函数的一个非紧凑的欧几里德D3-膜在背景超引力解，在无穷远的固定边界条件。
We consider $d=3$, $\mathcal{N}=2$ gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, $Σ_g$, with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a $D=11$ supergravity dual of the form AdS$_2\times Y_9$, with electric four-form flux and where $Y_9$ is topologically a fibration of a Sasakian $Y_7$ over $Σ_g$. These $D=11$ solutions are also expected to arise as the near horizon li…
We study vacua of N = 4 half-maximal gauged supergravity in five dimensions and determine crucial properties of the effective theory around the vacuum. The main focus is on configurations with exactly two broken supersymmetries, since they frequently appear in consistent truncations of string theory and supergravity. Evaluating one-loop corrections to the Chern-Simons terms we find necessary conditions to ensure that a consistent truncation also gives rise to a proper effective action of an underlying more fundamental theory. To obtain concrete examples, we determine the N=4 action of M-theory…
Consistent Truncations from Duality Symmetries and Desingularization of Orbifold Uplifts
Mandelstam Institute for Theoretical Physics, School of Physics, University of the Witwatersrand（维特沃特斯兰德大学物理学院曼德尔斯坦理论物理研究所）；Université Libre de Bruxelles (ULB)（布鲁塞尔自由大学）；International Solvay Institutes（国际索尔维研究所）；Department of Applied Science and Technology, Politecnico di Torino（都灵理工大学应用科学与技术系）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）
We consider supersymmetric AdS$_3 \times Y_7$ and AdS$_2 \times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively, that are holographically dual to SCFTs with $(0,2)$ supersymmetry in two dimensions and $\mathcal{N}=2$ supersymmetry in one dimension. The geometry of $Y_{2n+1}$, which can be defined for $n\ge 3$, shares many similarities with Sasaki-Einstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only…
We continue our study of a general class of $\mathcal{N}=2$ supersymmetric $AdS_3\times Y_7$ and $AdS_2\times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively. The geometry of the internal spaces is part of a general family of "GK geometries", $Y_{2n+1}$, $n\ge 3$, and here we study examples in which $Y_{2n+1}$ fibres over a Kähler base manifold $B_{2k}$, with toric fibres. We show that the flux quantization conditions, and an action function that determines the supersymmetric $R$-symmetry Killing vector of a geometry, may all be written in terms of the "master volume" of the f…
The giant graviton expansion in AdS$_5\times$SE$_5$
Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova and INFN Sezione di Padova（帕多瓦大学伽利略·伽利莱物理与天文系及意大利国家核物理研究所帕多瓦分部）；Leinweber Institute for Theoretical Physics, University of Michigan, Ann Arbor（密歇根大学莱因韦伯理论物理研究所）；Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University（首尔大学物理天文学系及理论物理中心）
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…
