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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.
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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.
We construct dynamical black hole solutions with a helical symmetry in AdS$_5$, called black resonators, as well as their horizonless limits, called geons. We introduce a cohomogeneity-1 metric describing a class of black resonators and geons whose isometry group is $Rtimes SU(2)$. This allows us to study them in a wide range of parameters. We obtain the phase diagram for the black resonators, geons, and Myers-Perry-AdS$_5$, where the black resonators emerge from the onset of a superradiant instability of the Myers-Perry-AdS$_5$ with equal angular momenta and are connected to the geons in the small horizon limit. The angular velocities of the black resonators always satisfy $Omega>1$ in units of the AdS radius. A black resonator is shown to have higher entropy than a Myers-Perry-AdS$_5$ black hole with the same asymptotic charges. This implies that the Myers-Perry-AdS$_5$ can dynamically evolve into the black resonator under the exact $SU(2)$-symmetry although its endpoint will be further unstable to $SU(2)$-violating perturbations.
In this work we explore the effect of rotation in the size of a traversable wormhole obtained via a double trace boundary deformation. We find that at fixed temperature the size of the wormhole increases with the angular momentum $J/Mell$. The amount of information that can be sent through the wormhole increases as well. However, for the type of interaction considered, the wormhole closes as the temperature approaches the extremal limit. We also briefly consider the scenario where the boundary coupling is not spatially homogeneous and show how this is reflected in the wormhole opening.
Minimal $D=5$ supergravity admits asymptotically globally AdS$_5$ gravitational solitons (strictly stationary, geodesically complete spacetimes with positive mass). We show that, like asymptotically flat gravitational solitons, these solutions satisfy mass and mass variation formulas analogous to those satisfied by AdS black holes. A thermodynamic volume associated to the non-trivial topology of the spacetime plays an important role in this construction. We then consider these solitons within the holographic ``complexity equals action and ``complexity equals volume conjectures as simple examples of spacetimes with nontrivial rotation and topology. We find distinct behaviours for the volume and action, with the counterterm for null boundaries playing a significant role in the latter case. For large solitons we find that both proposals yield a complexity of formation proportional to a power of the thermodynamic volume, $V^{3/4}$. In fact, up to numerical prefactors, the result coincides with the analogous one for large black holes.
We study a giant magnon and a spike solution for the string rotating on AdS(4) X CP**3 geometry. We consider rigid rotating fundamental string in the SU(2) X SU(2) sector inside the CP**3 and find out the general form of all the conserved charges. We find out the dispersion relation corresponding to both the known giant magnon and the new spike solutions. We further study the finite size correction in both cases.
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