Deformations of special geometry: in search of the topological string

The topological string captures certain superstring amplitudes which are also encoded in the underlying string effective action. However, unlike the topological string free energy, the effective action that comprises higher-order derivative couplings is not defined in terms of duality covariant variables. This puzzle is resolved in the context of real special geometry by introducing the so-called Hesse potential, which is defined in terms of duality covariant variables and is related by a Legendre transformation to the function that encodes the effective action. It is demonstrated that the Hesse potential contains a unique subsector that possesses all the characteristic properties of a topological string free energy. Genus $g\leq3$ contributions are constructed explicitly for a general class of effective actions associated with a special-K\"ahler target space and are shown to satisfy the holomorphic anomaly equation of perturbative type-II topological string theory. This identification of a topological string free energy from an effective action is primarily based on conceptual arguments and does not involve any of its more specific properties. It is fully consistent with known results. A general theorem is presented that captures some characteristic features of the equivalence, which demonstrates at the same time that non-holomorphic deformations of special geometry can be dealt with consistently.Comment: 44 pages, LaTex; v2, v3: minor text improvement

On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes

In this paper we elaborate on the relation between the entropy formula of Wald and the "entropy function" method proposed by A. Sen. For spherically symmetric extremal black holes, it is shown that the expression of extremal black hole entropy given by A. Sen can be derived from the general entropy definition of Wald, without help of the treatment of rescaling the AdS_2 part of near horizon geometry of extremal black holes. In our procedure, we only require that the surface gravity approaches to zero, and it is easy to understand the Legendre transformation of f, the integration of Lagrangian density on the horizon, with respect to the electric charges. Since the Noether charge form can be defined in an "off-shell" form, we define a corresponding entropy function, with which one can discuss the attractor mechanism for extremal black holes with scalar fields.Comment: v3: Revtex4, 19 pages, discussion added, mistakes corrected, final version; to appear in Phys. Rev.

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Editores técnicos: Marcílio José Thomazini, Elenice Fritzsons, Patrícia Raquel Silva, Guilherme Schnell e Schuhli, Denise Jeton Cardoso, Luziane Franciscon. EVINCI. Resumos

Black hole entropy functions and attractor equations

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N=2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions.Comment: 21 pages,LaTeX,minor change

The world-sheet corrections to dyons in the Heterotic theory

All the linear alpha-prime corrections, however excluding the gravitational Chern-Simons correction, are studied in the toroidally compactified critical Heterotic string theory. These corrections are computed to the entropy for a BPS static spherical four dimensional dyonic black hole which represents a wrapped fundamental string carrying arbitrary winding and momentum charges along one cycle in the presence of KK-monopole and H-monopole charges associated to another cycle. It is verified that after the inclusion of the gravitational Chern-Simons corrections [hep-th/0608182], all the linear alpha-prime corrections to the entropy for the supersymmetric dyon can be reproduced by the inclusion of only the Gauss-Bonnet Lagrangian to the supergravity approximation of the induced Lagrangian.Comment: JHEP style, 17 Pages; v2: a typo corrected ; v3: The coupling of the gravitational Chern-Simons terms to the three form field strength taken into account. The conclusion correcte

Processo de lavagem aumenta a incidência da podridão-mole em raízes de cenoura.

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