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The degeneracies of 1/4 BPS states with unit torsion in heterotic string theory compactified on a six torus are given in terms of the Fourier coefficients of the reciprocal of the Igusa cusp Siegel modular form Φ 10 of weight 10. We use the symplectic symmetries of the latter to construct a fine-grained Rademacher-type expansion which expresses these BPS degeneracies as a regularized sum over residues of the poles of 1 / Φ 10 . The construction uses two distinct SL (2 , Z) subgroups of Sp (2 , Z) which encode multiplier systems, Kloosterman sums and Eichler integrals appearing therein. Additionally, it shows how the polar data are explicitly built from the Fourier coefficients of 1 / η 24 by means of a continued fraction structure. [ABSTRACT FROM AUTHOR]

We use the exact degeneracy formula of single-centred 1 4 BPS dyonic black holes with unit torsion in 4D N = 4 toroidally compactified heterotic string theory to improve on the existing formulation of the corresponding quantum entropy function obtained using supersymmetric localization. The result takes the form of a sum over Euclidean backgrounds including orbifolds of the Euclidean AdS 2 × S 2 attractor geometry. Using an N = 2 formalism, we determine the explicit form of the Abelian gauge potentials supporting these backgrounds. We further show how a rewriting of the degeneracy formula is amenable, at a semi-classical level, to a gravitational interpretation involving 2D Euclidean wormholes. This alternative picture is useful to elucidate different aspects of the gravitational path integral capturing the microstate degeneracies. We also comment on the relation between the associated 1D holographic models. [ABSTRACT FROM AUTHOR]

In this note, we explore holographic attributes of four-dimensional near-extremal Reissner-Nordstrom black hole solutions in ungauged N = 2 supergravity theories at the two-derivative level by recasting them as a specific first-order deformation in solution space, associated with an infinitesimal Harrison transformation, of black holes in an AdS2 space-time. Specifically, we use this link to exhibit how bulk properties, such as mass and entropy, of four-dimensional near-extremal black holes are holographically encoded in the one-dimensional boundary theory dual to gravity in an infinitesimally deformed AdS2 space-time. We do so for the case of four-dimensional near-extremal black holes that arise as deformations in solution space of BPS black holes by changing the non-extremality parameter. For these near-extremal black holes, we further show that the nAdS2 attractor mechanism can be recast as a specific deformation of the BPS flow equations in four dimensions. Additionally, we also discuss time-dependent perturbations of the four-dimensional near-extremal Reissner-Nordstrom solutions from a two-dimensional point of view. [ABSTRACT FROM AUTHOR]

We use continued fractions to perform a systematic and explicit characterization of the decays of two-centred dyonic black holes in 4D N = 4 heterotic ℤN CHL models. Thereby we give a new exact solution for the problem of counting decadent dyons in these models. [ABSTRACT FROM AUTHOR]

We approach the problem of constructing an explicit holographic dictionary for the AdS2/CFT1 correspondence in the context of higher derivative gravitational actions in AdS2 space-times. These actions are obtained by an S2 reduction of four-dimensional N = 2 Wilsonian effective actions with Weyl squared interactions restricted to constant scalar backgrounds. BPS black hole near-horizon space-times fall into this class of backgrounds, and by identifying the boundary operators dual to the bulk fields, we explicitly show how the Wald entropy of the BPS black hole is holographically encoded in the anomalous transformation of the operator dual to a composite bulk field. Additionally, using a 2d/3d lift, we show that the CFT holographically dual to AdS2 is naturally embedded in the chiral half of the CFT2 dual to the AdS3 space-time, and we identify the specific operator in CFT1 that encodes the chiral central charge of the CFT2. [ABSTRACT FROM AUTHOR]

Extending recent results in N = 2 string compactifications, we propose that the holomorphic anomaly equation satisfied by the modular completions of the generating functions of refined BPS indices has a universal structure independent of the number N of supersymmetries. We show that this equation allows to recover all known results about modularity (under SL(2, ℤ) duality group) of BPS states in N = 4 string theory. In particular, we reproduce the holomorphic anomaly characterizing the mock modular behavior of quarter-BPS dyons and generalize it to the case of non-trivial torsion invariant. [ABSTRACT FROM AUTHOR]

We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions. [ABSTRACT FROM AUTHOR]

The Kerr/CFT correspondence employs the Cardy formula to compute the entropy of the left moving CFT states. This computation, which correctly reproduces the Bekenstein-Hawking entropy of the four-dimensional extremal Kerr black hole, is performed in a regime where the temperature is of order unity rather than in a high-temperature regime. We show that the comparison of the entropy of the extreme Kerr black hole and the entropy in the CFT can be understood within the Cardy regime by considering a D0-D6 system with the same entropic properties. [ABSTRACT FROM AUTHOR]

We generalize the computations of [1] to generate long wavelength, asymptotically locally AdS5 solutions to the Einstein-dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity , our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parameterized by four-velocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence. [ABSTRACT FROM AUTHOR]