We study the spectrum of the scalar Laplacian on the five-dimensional toric Sasaki-Einstein manifolds Y^{p,q}. The eigenvalue equation reduces to Heun's equation, which is a Fuchsian equation with four regular singularities. We show that the ground states, which are given by constant solutions of Heun's equation, are identified with BPS states corresponding to the chiral primary operators in the dual quiver gauge theories. The excited states correspond to non-trivial solutions of Heun's equation. It is shown that these reduce to polynomial solutions in the near BPS limit.
We analyze the transverse Kähler-Ricci flow equation on Sasaki-Ein\-stein space $Y^{p,q}$. Explicit solutions are produced representing new five-dimensional Sasaki structures. Solutions which do not modify the transverse metric preserve the Sasaki-Einstein feature of the contact structure. If the transverse metric is altered, the deformed metrics remain Sasaki, but not Einstein.
Holographic spectral functions for Sasaki-Einstein 5-manifolds
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；School of Physics and Shing-Tung Yau Center, Southeast University（东南大学物理学院及施一公中心）
Methods of Hamiltonian dynamics are applied to study the geodesic flow on the resolved conifolds over Sasaki-Einstein space $T^{1,1}$. We construct explicitly the constants of motion and prove complete integrability of geodesics in the five-dimensional Sasaki-Einstein space $T^{1,1}$ and its Calabi-Yau metric cone. The singularity at the apex of the metric cone can be smoothed out in two different ways. Using the small resolution the geodesic motion on the resolved conifold remains completely integrable. Instead, in the case of the deformation of the conifold the complete integrability is lost…
A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure
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。
We revisit non-rotating, dyonically charged, and supersymmetric AdS$_4$ black holes, which are solutions of $\mathcal{N}=2$ gauged supergravity with vector- and hyper-multplets. Uplifting the near horizon solutions to $D=11$ supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS$_4$ black holes correspond to AdS$_2$ solutions with electric and magnetic baryonic fluxes in $D=11$ supergravity. We identify the off-shell AdS$_4$ black hole solutions with parameters of $D=11$ AdS$_2$ solutions without imposing the equations of motion. We calculate the entropy of dyonic…
On the non-BPS string solutions in Sasaki-Einstein gauge/gravity duality
我们对AdS_5 x Ypq中的几个弦解进行了广泛的分析，发现了它们的能量-自旋关系的一些有趣的性质。它们的能量总是依赖于表征这些流形的参数a（p，q）。弦解的这个参数的范围受到解应该满足的Sasaki-Einstein约束的约束。因此，我们找到的一些弦解对整个Ypq流形类都是无效的。对于我们的一些解，当a（p，q）的最大允许值对应于接近Ypq中的压缩球的极点的弦时，它们在这个极限处的能量接近BPS。因此，整个Sasaki-Einstein流形类中的某些非BPS弦解可以成为特定流形中的BPS。对于具有这种性质的解，我们指出这种行为与弦在流形上其他方向上的运动无关。我们期望在场论中，对应于这些半经典弦的类属算符在某些箭点处变成BPS。
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…
In this note we give an explicit construction of Sasaki-Einstein metrics on a class of simply connected 7-manifolds with the rational cohomology of the 2-fold connected sum of $S^2\times S^5$. The homotopy types are distinguished by torsion in $H^4$.
In this paper, we calculate the topological free energy for a number of ${\mathcal N} \geq 2$ Yang-Mills-Chern-Simons-matter theories at large $N$ and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the partition function of the theory on $S^2 \times S^1$ with a topological A-twist along $S^2$ and can be reduced to a matrix integral by exploiting the localization technique. The theories of our interest are dual to a variety of Calabi-Yau four-fold singularities, including a product of two asymptotically locally Euclidean singularities and the cone over var…
我们表明，通过采取一定的标度限制的欧几里德形式的Plebanski-Demianski度量得到一个家庭的本地环面Kahler-Einstein度量。这些可以用来构造5维的局部Sasaki-Einstein度量，它们是Y^{p，q}流形的推广。事实上，我们发现，这些指标是同构的Cvetic，Lu，Page和教皇最近发现的。我们证明了相应的光滑Sasaki-Einstein流形族都具有拓扑S^2 x S^3。最后，我们建立了描述翘曲形式的卡-丘锥的方程，支持（2，1）三形式通量。
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 consider supergravity in five-dimensional Anti-De Sitter space $AdS_{5}$ with minimal supersymmetry, encoded by a Sasaki-Einstein metric on a five-dimensional compact manifold $M$. Our main result reveals how the Sasaki-Einstein metric emerges from a canonical state in the dual CFT, defined by a superconformal gauge theory in four dimensional Minkowski space $\mathbb{R}^{3,1}$in the t'Hooft limit where the rank $N$ tends to infinity. We obtain explicit finite $N-$approximations to the Sasaki-Einstein metric, expressed in terms of a canonical (i.e. background free) BPS-state on the gauge the…
On the pulsating strings in Sasaki-Einstein spaces
研究了AdS_5 x Y^{p，q}和AdS_5 x L^{p，q，r}中的脉动弦类.利用脉动弦组态的广义解，我们用Heun函数找到了该类的新解，并导出了AdS_5 x T^{1，1}的特殊情况，这在arXiv：1006.1539 [hep-th]中已经分析过.不幸的是，Heun函数的研究仍然很少，我们不能准经典地解释理论，并获得第一个修正的能量。由于AdS/CFT对应，后者可以给出规范理论对偶N=1超共形场论中算符的反常维数.
