On Quantum Special Kaehler Geometry

We compute the effective black hole potential V of the most general N=2, d=4 (local) special Kaehler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of ``flat'' directions of V at its critical points. Furthermore, we elucidate the role of the sectional curvature at the non-supersymmetric critical points of V, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the non-symmetricity of the considered quantum perturbative special Kaehler geometry.Comment: 1+43 pages; v2: typo corrected in the curvature of Jordan symmetric sequence at page 2

Spin-dependent Fano resonance induced by conducting chiral helimagnet contained in a quasi-one-dimensional electron waveguide

Fano resonance appears for conduction through an electron waveguide containing donor impurities. In this work, we consider the thin-film conducting chiral helimagnet (CCH) as the donor impurity in a one-dimensional waveguide model. Due to the spin spiral coupling, interference between the direct and intersubband transmission channels gives rise to spin-dependent Fano resonance effect. The spin-dependent Fano resonance is sensitively dependent on the helicity of the spiral. By tuning the CCH potential well depth and the incident energy, this provides a potential way to detect the spin structure in the CCH.Comment: 14 pages, 6 figure

BPS black holes, the Hesse potential, and the topological string

The Hesse potential is constructed for a class of four-dimensional N=2 supersymmetric effective actions with S- and T-duality by performing the relevant Legendre transform by iteration. It is a function of fields that transform under duality according to an arithmetic subgroup of the classical dualities reflecting the monodromies of the underlying string compactification. These transformations are not subject to corrections, unlike the transformations of the fields that appear in the effective action which are affected by the presence of higher-derivative couplings. The class of actions that are considered includes those of the FHSV and the STU model. We also consider heterotic N=4 supersymmetric compactifications. The Hesse potential, which is equal to the free energy function for BPS black holes, is manifestly duality invariant. Generically it can be expanded in terms of powers of the modulus that represents the inverse topological string coupling constant, $g_s$, and its complex conjugate. The terms depending holomorphically on $g_s$ are expected to correspond to the topological string partition function and this expectation is explicitly verified in two cases. Terms proportional to mixed powers of $g_s$ and $\bar g_s$ are in principle present.Comment: 28 pages, LaTeX, added comment

How Does a Fundamental String Stretch its Horizon?

It has recently been shown that if we take into account a class of higher derivative corrections to the effective action of heterotic string theory, the entropy of the black hole solution representing elementary string states correctly reproduces the statistical entropy computed from the degeneracy of elementary string states. So far the form of the solution has been analyzed at distance scales large and small compared to the string scale. We analyze the solution that interpolates between these two limits and point out a subtlety in constructing such a solution due to the presence of higher derivative terms in the effective action. We also study the T-duality transformation rules to relate the moduli fields of the effective field theory to the physical compactification radius in the presence of higher derivative corrections and use these results to find the physical radius of compactification near the horizon of the black hole. The radius approaches a finite value even though the corresponding modulus field vanishes. Finally we discuss the non-leading contribution to the black hole entropy due to space-time quantum corrections to the effective action and the ambiguity involved in comparing this result to the statistical entropy.Comment: LaTeX file, 38 pages; v2: minor changes and added reference

Effects due to a scalar coupling on the particle-antiparticle production in the Duffin-Kemmer-Petiau theory

The Duffin-Kemmer-Petiau formalism with vector and scalar potentials is used to point out a few misconceptions diffused in the literature. It is explicitly shown that the scalar coupling makes the DKP formalism not equivalent to the Klein-Gordon formalism or to the Proca formalism, and that the spin-1 sector of the DKP theory looks formally like the spin-0 sector. With proper boundary conditions, scattering of massive bosons in an arbitrary mixed vector-scalar square step potential is explored in a simple way and effects due to the scalar coupling on the particle-antiparticle production and localization of bosons are analyzed in some detail

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