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Register a new userRotating multi-charge spindles and their microstates
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Some AdS$_3 times M_7$ type IIB vacua have been recently proposed to arise from D3-branes wrapped on a spindle, a sphere with conical singularities at the poles. We explicitly construct a generalization of these solutions corresponding to a class of electrically charged and rotating supersymmetric black strings in AdS$_5 times S^5$ with general magnetic fluxes on the spindle. We then perform a counting of their microstates using the charged Cardy formula. To this purpose, we derive the general form of the anomaly polynomial of the dual $mathcal{N} = (0 , 2)$ CFT in two dimensions and we show that it can be obtained via a simple gluing procedure.
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We construct families of supersymmetric AdS$_3times Y_7$ and AdS$_3times Y_8$ solutions to type IIB string theory and M-theory, respectively. Here $Y_7$ is an $S^5$ fibration over $Sigma$, while $Y_8$ is an $S^4$ fibration over $Sigma_gtimes Sigma$, where $Sigma_g$ is a Riemann surface of genus $g>1$ and $Sigma$ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of $N$ D3-branes wrapped on $Sigma$ and $N$ M5-branes wrapped on $Sigma_gtimes Sigma$, respectively. These are holographically dual to $d=2$, $(0,2)$ SCFTs, and we show that the central charge and superconformal R-symmetry of the gravity solutions agree with dual field theory calculations.
We provide a general formula for the refined topologically twisted index of $mathcal{N}=1$ gauge theories living on the world-volume of D3-branes at conical Calabi-Yau singularities in the Cardy limit. The index is defined as the partition function on $T^2 times S^2_omega$, with a partial topological twist and a $Omega$-deformation along $S^2$, in the presence of background magnetic fluxes and fugacities for the global symmetries and can be used to study the properties of a class of BPS black strings. To this purpose, we find rotating domain-wall solutions of five-dimensional gauged supergravity interpolating between AdS$_5$ and a near horizon region consisting of a warped fibration of BTZ over a sphere. We explicitly construct rotating domain-walls that can be embedded in AdS$_5 times S^5$ by uplifting a class of four-dimensional rotating black holes. We then provide a microscopic explanation of the entropy of such black holes by using the refined topologically twisted index of $mathcal{N}=4$ super Yang-Mills.
We study solutions in the Plebanski--Demianski family which describe an accelerating, rotating and dyonically charged black hole in $AdS_4$. These are solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological constant and hence minimal $D=4$ gauged supergravity. It is well known that when the acceleration is non-vanishing the $D=4$ black hole metrics have conical singularities. By uplifting the solutions to $D=11$ supergravity using a regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the $D=11$ solutions incorporate an $SE_7$ fibration over a two-dimensional weighted projective space, $mathbb{WCP}^1_{[n_-,n_+]}$, also known as a spindle, which is labelled by two integers that determine the conical singularities of the $D=4$ metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric $AdS_2times Y_9$ solutions of $D=11$ supergravity, which generalise a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain ${cal N}=2$, $d=3$ quiver gauge theories compactified on a spinning spindle with appropriate magnetic flux.
We consider ensemble averaged theories with discrete random variables. We propose a suitable measure to do the ensemble average. We also provide a mathematical description of such ensemble averages of theories in terms of Poisson point processes. Moreover, we demonstrate that averaging theories of this type has an equivalent description as tracing over parts of the microscopic degrees of freedom in a suitable continuous limit of a single microscopic theory. The results from both approaches can be identified with Liouville gravity, of which we further address some implications on the microscopic theory, including venues to look for quantum effects from the view point of the averaged theory. Generalizations to other point processes are also discussed.
A large class of two dimensional quantum gravity theories of Jackiw-Teitelboim form have a description in terms of random matrix models. Such models, treated fully non-perturbatively, can give an explicit and tractable description of the underlying ``microstate degrees of freedom. They play a prominent role in regimes where the smooth geometrical picture of the physics is inadequate. This is shown using a natural tool for extracting the detailed microstate physics, a Fredholm determinant ${rm det}(mathbf{1}{-}mathbf{ K})$. Its associated kernel $K(E,E^prime)$ can be defined explicitly for a wide variety of JT gravity theories. To illustrate the methods, the statistics of the first several energy levels of a non-perturbative definition of JT gravity are constructed explicitly using numerical methods, and the full quenched free energy $F_Q(T)$ of the system is computed for the first time. These results are also of relevance to quantum properties of black holes in higher dimensions.
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