We study the superconfomal index of four-dimensional toric quiver gauge theories using a Bethe-Ansatz approach recently applied by Benini and Milan. Relying on a particular set of solutions to the corresponding Bethe Ansatz equations we evaluate the superconformal index in the large N limit, thus avoiding to take any Cardy-like limit. We present explicit results for theories arising as a stack of N D3 branes at the tip of toric Calabi-Yau cones: the conifold theory, the suspended pinch point gauge theory, the first del Pezzo theory and Y p,q quiver gauge theories. For generic quiver gauge theories we find a particular correction to the superconformal index in the Cardy limit that happens to vanish in the case of N = 4 supersymmetric Yang-Mills. We estimate how such correction affects the entropy of the would be dual electrically charged rotating AdS 5 black holes.

We systematically study various sub-leading structures in the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU(N) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d $$ \mathcal{N} $$ N = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS5 black holes and could be tested by low-energy IIB supergravity.

We investigate the Bethe-Ansatz (BA) approach to the superconformal index of N = 4 supersymmetric Yang-Mills with SU(N ) gauge group in the context of finite rank, N . We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations (BAE) in recovering the exact index for N = 2, 3. We classify the BAE solutions as standard (corresponding to a freely acting orbifold T 2 /Z m × Z n ) and nonstandard. For N = 2, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, for N ≥ 3, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

We investigate the Bethe-Ansatz approach to the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills with SU(N) gauge group in the context of finite rank, N. We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations in recovering the exact index for N = 2, 3. We classify the Bethe-Ansatz Equations solutions as standard (corresponding to a freely acting orbifold T2/ℤm× ℤn) and non-standard. For N = 2, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, for N ≥ 3, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

Thick granular flows are essential to many natural and industrial phenomena. Experimentally, it has been well established that the grain velocity profile is linear from the free surface to a certain depth, after which it decreases exponentially in the so-called "creep region". In this paper we obtain an exponential velocity profile based on the force balance of a grain near a wall, where the Janssen effect and the non-locality of interactions between grains are considered. When experimental parameters such as flow angles and friction coefficients are introduced in our model, it is able to reproduce experimental creep velocity profiles previously reported in the literature.

Methylammonium lead iodide (CH 3 NH 3 PbI 3 ) is one of the most attractive materials for optoelectronic applications, and it is the most typical absorber in perovskite solar cells, which are unprecedentedly successful devices in terms of power conversion efficiency. In this work, the conductivity and capacitance spectra of symmetrically contacted Au/CH 3 NH 3 PbI 3 /Au thick pellets are measured via impedance spectroscopy at different temperatures in dark equilibrium. The experimental conductivity spectra are parameterized and showed to follow the formalism of hopping DC conductivity in the CH 3 NH 3 PbI 3 bulk. The presence of several regimes for the general Jonscher's "universal" conductivity-frequency response is highlighted and associated with the ionic-electronic overlapping conductivities. For the capacitance spectra, the general features of electrode polarization capacitance at the CH 3 NH 3 PbI 3 /Au interfaces are identified but yet are found to be in disagreement with some trends of classical ionic conductivity models, unable to separate different contributions. Accordingly, an analytical model is proposed accounting for hopping processes where the low frequency activation energy is split into ionic and electronic components. Our parameterizations and analytical model discern between the bulk/interface and ionic/electronic phenomena and estimate the multiple activation energies in this hybrid halide perovskite.

We explore the notion of c-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic c-function and thereby establish a holographic c-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate c-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d N = 4 SYM and compactifications of 6d N = (2, 0) theories.

We explore the notion of c-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic c-function and thereby establish a holographic c-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate c-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d $$ \mathcal{N} $$ N = 4 SYM and compactifications of 6d $$ \mathcal{N} $$ N = (2, 0) theories.