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Freudenthal duality (FD) is a non-linear symmetry of the Bekenstein-Hawking entropy of extremal dyonic black holes (BHs) in Maxwell-Einstein-scalar theories in four space-time dimensions realized as an anti-involutive map in the symplectic space of electric-magnetic BH charges. In this paper, we generalize FD to the class of rotating (stationary) extremal BHs, both in the under- and over-rotating regime, defining a (generalized) rotating FD (generally, non-anti-involutive) map (RFD), which also acts on the BH angular momentum. We prove that the RFD map is unique, and we compute the explicit expression of its non-linear action on the angular momentum itself. Interestingly, in the non-rotating limit, RFD bifurcates into the usual, non-rotating FD branch and into a spurious branch, named "golden" branch, mapping a non-rotating (static) extremal BH to an under-rotating (stationary) extremal BH, in which the ratio between the angular momentum and the non-rotating entropy is the square root of the golden ratio. Finally, we investigate the possibility of inducing transitions between the under- and over- rotating regimes by means of RFD, obtaining a no-go result. [ABSTRACT FROM AUTHOR]

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in N = 8 string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima. [ABSTRACT FROM AUTHOR]

Freudenthal duality is, as of now, the unique non-linear map on electric-magnetic (e.m.) charges which is a symmetry of the Bekenstein-Hawking entropy of extremal black holes, displaying the Attractor Mechanism (possibly, up to some flat directions) in Maxwell-Einstein-scalar theories in four space-time dimensions and with non-trivial symplectic e.m. duality. In this paper, we put forward an effective approach to a consistent generalization of Freudenthal duality to near-extremal black holes, whose entropy is obtained within a Jackiw-Teitelboim gravity upon dimensional reduction. We name such a generalization near-extremal Freudenthal duality. Upon such a duality, two near-extremal black holes with two different (and both small) temperatures have the same entropy when their e.m. charges are related by a Freudenthal transformation. By exploiting Descartes' rule of signs as well as Sturm's Theorem, we show that our formulation of the near-extremal Freudenthal duality is analytical and unique. [ABSTRACT FROM AUTHOR]

We compute the exact retarded Green’s functions in thermal CFTs with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in AdS spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville CFT. The connection formulae associated with the boundary conditions imposed on the bulk field equations yield the exact thermal correlators in the boundary CFT. [ABSTRACT FROM AUTHOR]

We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large D limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of O (D0). Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in 1/D. We also obtain the equations governing the dual membranes up to the first sub-leading order in 1/D. [ABSTRACT FROM AUTHOR]

Copper is crucial for carrying out normal physiological functions in all higher life forms. Copper Transporter 1 (CTR1) is the high-affinity copper importer found in all eukaryotic organisms. The copper transporter family primarily comprises ~ six members (CTR1-6) and the related members share high sequence homology with CTR. However, with the exception of CTR1, not all six CTRs are present in every organism. Despite having a simple trimeric channel structure, CTR1 and other members exhibit some unique regulatory properties. In the present review, we attempt to understand the diversity and similarity of regulation and functioning of the members of this copper transporter family. [ABSTRACT FROM AUTHOR]

We study the effect of Freudenthal duality on supersymmetric extremal black hole attractors in , ungauged supergravity. Freudenthal duality acts on the dyonic black hole charges as an anti-involution which keeps the black hole entropy and the critical points of the effective black hole potential invariant. We analyze its effect on the recently discovered distinct, mutually exclusive phases of axionic supersymmetric black holes, related to the existence of nontrivial involutory constant matrices. In particular, we consider a supersymmetric black hole and we explicitly Freudenthal-map it to a supersymmetric black hole. We thus show that the charge representation space of a supersymmetric black hole also contains mutually exclusive domains. [ABSTRACT FROM AUTHOR]

In this paper, we consider the four-dimensional N = 2 supergravity theory arising from the compactification of type IIA string theory on a Calabi-Yau manifold. We analyze the supersymmetric flow equations for static, spherically symmetric, single-centered black holes. These flow equations are solved by a set of algebraic equations involving the holomorphic sections and harmonic functions. We examine black hole configurations with D0- D4- D6 charge for which the most general solution of these algebraic equations are considered. Though the black hole solution is unique for a given value of the charges, we find new phases of the black hole solutions upon varying them. [ABSTRACT FROM AUTHOR]

We use holography to compute the exact form of retarded Green's functions for a scalar operator with conformal dimension ∆ in a thermal CFT and in its related counterpart with chemical potential in R1 × H3. In our analysis, we recast the wave equation of a scalar field in the normal form of Heun's equation in the dual gravity theories described by the AdS hyperbolic blackhole and its charged version. Heun's equation is identified to the semiclassical limit of the BPZ equation for a five-point correlator with one degenerate field insertion in the Liouville theory on the Riemann sphere. The crossing symmetry of conformal block in the Liouville theory eventually gives rise to a set of connection formulas among the solutions of Heun's equation evaluated at different regular singularities. We use the connection formula to reproduce the leading order behaviors of the scalar field near the horizon as well as near the boundary and achieve the exact form of the retarded thermal Green's function. We show a recipe to obtain the exact retarded Green's function for a thermal CFT dual to AdS blackbrane from a high-temperature limit accompanied by a complex mapping on AdS hyperbolic blackhole. Moreover, we show the retarded Green's function for the boundary CFT of Rindler AdS spacetime admits a free integer parameter. [ABSTRACT FROM AUTHOR]

In this paper we discuss the uniqueness of supersymmetric attractors in four-dimensional N = 2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness. [ABSTRACT FROM AUTHOR]