Black Holes and Critical Points in Moduli Space

We study the stabilization of scalars near a supersymmetric black hole horizon using the equation of motion of a particle moving in a potential and background metric. When the relevant 4-dimensional theory is described by special geometry, the generic properties of the critical points of this potential can be studied. We find that the extremal value of the central charge provides the minimal value of the BPS mass and of the potential under the condition that the moduli space metric is positive at the critical point. We relate these ideas to the Weinhold and Ruppeiner metrics introduced in the geometric approach to thermodynamics and used for study of critical phenomena.Comment: 19 pages, Late

Nonabelian gauge field dynamics on matrix D-branes

We construct a calculational scheme for handling the matrix ordering problems connected with the appearance of D-brane positions taking values in the same Lie algebra as the nonabelian gauge field living on the D-brane. The formalism is based on the use of an one-dimensional auxiliary field living on the boundary of the string world sheet and taking care of the order of the matrix valued fields. The resulting system of equations of motion for both the gauge field and the D-brane position is derived in lowest order of the $\alpha'$ -expansion.Comment: 14 pages, Latex, 2 figures, including epsfig.sty, a wrong reference number correcte

Classical and quantum N=2 supersymmetric black holes

We use heterotic/type-II prepotentials to study quantum/classical black holes with half the $N=2, D=4$ supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula is given by the tree-level entropy formula with the tree-level coupling constant replaced by the perturbative coupling constant. In the case of type-II compactifications, we display a new entropy/area formula associated with axion-free black-hole solutions, which depends on the electric and magnetic charges as well as on certain topological data of Calabi--Yau three-folds, namely the intersection numbers, the second Chern class and the Euler number of the three-fold. We show that, for both heterotic and type-II theories, there is the possibility to relax the usual requirement of the non-vanishing of some of the charges and still have a finite entropy.Comment: 28 pages, LaTe

Supersymmetric dyonic black holes of IIA string on Six Torus

A class of four-dimensional static supersymmetric black hole solutions of effective supergravity Lagrangian of IIA superstring compactified on $T^6$ is constructed by explicitly solving Killing spinor equations (KSEs). These solutions are dyonic black holes parametrized by four charges, with dilaton and diagonal internal metric components as the only non-zero scalar fields, and preserve $1 \over 8$ of $N=8$ supersymmetry. The KSEs with only Neveu-Schwarz-Neveu-Schwarz charges relate spinors with opposite chirality from ten-dimensional view point, and have identical structures with KSEs of toroidally compactified heterotic string. We also find a solution with four Ramond-Ramond charges which is U-dual to the solution with four Neveu-Schwarz-Neveu-Schwarz charges, and corresponds to the intersecting D-brane configuration with two 2-branes and two 4-branes. A configuration with both Neveu-Schwarz-Neveu-Schwarz charges and Ramond-Ramond charges is also found. We show that the configurations T-dual to the above solutions are also solutions of the KSEs. The patterns of supersymmetry breaking are studied in detail.Comment: LaTeX with RevTeX, 41 page

Gauge Symmetry Enhancement and N = 2 Supersymmetric Quantum Black Holes in Heterotic String Vacua

N=2 supersymmetric quantum black holes in the heterotic S-T-U model are presented. In particular three classes of axion-free quantum black holes with half the N=2, D=4 supersymmetries unbroken are considered. First, these quantum black holes are investigated at generic points in moduli space. Then linearized non-abelian black holes are investigated representing a subset of non-abelian black hole solutions at critical points of perturbative gauge symmetry enhancement in moduli space. It is shown that the entropy of linearized non-abelian black holes can be obtained, starting at non-critical points in moduli space, by continuous variation of the moduli and a proper identification of the non-abelian charges.Comment: 20 pages, final revised versio

Kappa-Symmetry, Supersymmetry and Intersecting Branes

We present a new form of kappa-symmetry transformations for D-branes in which the dependence on the Born-Infeld field strength is expressed as a relative rotation on the left- and right-moving fields with opposite parameters. Then, we apply this result to investigate the supersymmetry preserved by certain intersecting brane configurations at arbitrary angles and with non-vanishing constant Born-Infeld fields. We also comment on the covariant quantization of the D-brane actions.Comment: Latex file. CERN preprint number correcte