The mixed black hole partition function for the STU model

We evaluate the mixed partition function for dyonic BPS black holes using the recently proposed degeneracy formula for the STU model. The result factorizes into the OSV mixed partition function times a proportionality factor. The latter is in agreement with the measure factor that was recently conjectured for a class of N=2 black holes that contains the STU model.Comment: 14 page

The holographic RG flow in a field theory on a curved background

As shown by Freedman, Gubser, Pilch and Warner, the RG flow in ${\cal N}=4$ super-Yang-Mills theory broken to an ${\cal N}=1$ theory by the addition of a mass term can be described in terms of a supersymmetric domain wall solution in five-dimensional ${\cal N}=8$ gauged supergravity. The FGPW flow is an example of a holographic RG flow in a field theory on a flat background. Here we put the field theory studied by Freedman, Gubser, Pilch and Warner on a curved $AdS_4$ background, and we construct the supersymmetric domain wall solution which describes the RG flow in this field theory. This solution is a curved (non Ricci flat) domain wall solution. This example demonstrates that holographic RG flows in supersymmetric field theories on a curved $AdS_4$ background can be described in terms of curved supersymmetric domain wall solutions.Comment: 14 pages, LaTe

Perturbative gravitational couplings and Siegel modular forms in D=4,N=2D=4,N=2 string models

We consider four-parameter $D=4,N=2$ string models with Hodge numbers $(4,214- 12n)$ and $(4,148)$, and we express their perturbative Wilsonian gravitational coupling $F_1$ in terms of Siegel modular forms.Comment: 8 pages, Latex 2.09, Contribution to the Proceedings of the 30th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, August 27-31, 199

Entropy function for rotating extremal black holes in very special geometry

We use the relation between extremal black hole solutions in five- and in four-dimensional N=2 supergravity theories with cubic prepotentials to define the entropy function for extremal black holes with one angular momentum in five dimensions. We construct two types of solutions to the associated attractor equations.Comment: 15 pages, minor change

Extremal non-BPS black holes and entropy extremization

At the horizon, a static extremal black hole solution in N=2 supergravity in four dimensions is determined by a set of so-called attractor equations which, in the absence of higher-curvature interactions, can be derived as extremization conditions for the black hole potential or, equivalently, for the entropy function. We contrast both methods by explicitly solving the attractor equations for a one-modulus prepotential associated with the conifold. We find that near the conifold point, the non-supersymmetric solution has a substantially different behavior than the supersymmetric solution. We analyze the stability of the solutions and the extrema of the resulting entropy as a function of the modulus. For the non-BPS solution the region of attractivity and the maximum of the entropy do not coincide with the conifold point.Comment: 19 pages, 4 figures, AMS-LaTeX, reference adde

Asymptotic degeneracy of dyonic N=4 string states and black hole entropy

It is shown that the asymptotic growth of the microscopic degeneracy of BPS dyons in four-dimensional N=4 string theory captures the known corrections to the macroscopic entropy of four-dimensional extremal black holes. These corrections are subleading in the limit of large charges and originate both from the presence of interactions in the effective action quadratic in the Riemann tensor and from non-holomorphic terms. The presence of the non-holomorphic corrections and their contribution to the thermodynamic free energy is discussed. It is pointed out that the expression for the microscopic entropy, written as a function of the dilaton field, is stationary at the horizon by virtue of the attractor equations.Comment: 16 pages Late

Holographic Gravitational Anomalies

In the AdS/CFT correspondence one encounters theories that are not invariant under diffeomorphisms. In the boundary theory this is a gravitational anomaly, and can arise in 4k+2 dimensions. In the bulk, there can be gravitational Chern-Simons terms which vary by a total derivative. We work out the holographic stress tensor for such theories, and demonstrate agreement between the bulk and boundary. Anomalies lead to novel effects, such as a nonzero angular momentum for global AdS(3). In string theory such Chern-Simons terms are known with exact coefficients. The resulting anomalies, combined with symmetries, imply corrections to the Bekenstein-Hawking entropy of black holes that agree exactly with the microscopic counting.Comment: 25 page

First-order flow equations for extremal black holes in very special geometry

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N=2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five- and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions.Comment: 21 pages. v2: Summary section adde

Deformation of Curved BPS Domain Walls and Supersymmetric Flows on 2d K\"ahler-Ricci Soliton

We consider some aspects of the curved BPS domain walls and their supersymmetric Lorentz invariant vacua of the four dimensional N=1 supergravity coupled to a chiral multiplet. In particular, the scalar manifold can be viewed as a two dimensional K\"ahler-Ricci soliton generating a one-parameter family of K\"ahler manifolds evolved with respect to a real parameter, $\tau$. This implies that all quantities describing the walls and their vacua indeed evolve with respect to $\tau$. Then, the analysis on the eigenvalues of the first order expansion of BPS equations shows that in general the vacua related to the field theory on a curved background do not always exist. In order to verify their existence in the ultraviolet or infrared regions one has to perform the renormalization group analysis. Finally, we discuss in detail a simple model with a linear superpotential and the K\"ahler-Ricci soliton considered as the Rosenau solution.Comment: 19 pages, no figures. Typos corrected. Published versio

Entropy Function for Heterotic Black Holes

We use the entropy function formalism to study the effect of the Gauss-Bonnet term on the entropy of spherically symmetric extremal black holes in heterotic string theory in four dimensions. Surprisingly the resulting entropy and the near horizon metric, gauge field strengths and the axion-dilaton field are identical to those obtained by Cardoso et. al. for a supersymmetric version of the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet term. We also study the effect of holomorphic anomaly on the entropy using our formalism. Again the resulting attractor equations for the axion-dilaton field and the black hole entropy agree with the corresponding equations for the supersymmetric version of the theory. These results suggest that there might be a simpler description of supergravity with curvature squared terms in which we supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.Comment: LaTeX file, 23 pages; v2: references added; v3: minor addition; v4: minor change