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

Discreteness of the spectrum of the compactified D=11 supermembrane with non-trivial winding

We analyze the Hamiltonian of the compactified D=11 supermembrane with non-trivial central charge in terms of the matrix model constructed recently by some of the authors. Our main result provides a rigorous proof that the quantum Hamiltonian of the supersymmetric model has compact resolvent and thus its spectrum consists of a discrete set of eigenvalues with finite multiplicity.Comment: 16 pages, final versio

Comments on the global constraints in light-cone string and membrane theories

In the light-cone closed string and toroidal membrane theories, we associate the global constraints with gauge symmetries. In the closed string case, we show that the physical states defined by the BRS charge satisfy the level-matching condition. In the toroidal membrane case, we show that the Faddeev-Popov ghost and anti-ghost corresponding to the global constraints are essentially free even if we adopt any gauge fixing condition for the local constraint. We discuss the quantum double-dimensional reduction of the wrapped supermembrane with the global constraints.Comment: 12 pages, typos corrected, to appear in JHE

Einstein-Cartan theory as a theory of defects in space-time

The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce the latter as a description of the equilibrium state of a three-dimensional continuum. Despite these important differences, an analogy is built on their common geometrical foundations, and it is shown that a space-time with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects. This formal analogy is useful for illustrating the geometrical concept of torsion by applying it to concrete physical problems. Moreover, the presentation of these theories using a common geometrical basis allows a deeper understanding of their foundations.Comment: 18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal of Physics, revised version with typos correcte

The heat kernel of the compactified D=11 supermembrane with non-trivial winding

We study the quantization of the regularized hamiltonian, $H$, of the compactified D=11 supermembrane with non-trivial winding. By showing that $H$ is a relatively small perturbation of the bosonic hamiltonian, we construct a Dyson series for the heat kernel of $H$ and prove its convergence in the topology of the von Neumann-Schatten classes so that $e^{-Ht}$ is ensured to be of finite trace. The results provided have a natural interpretation in terms of the quantum mechanical model associated to regularizations of compactified supermembranes. In this direction, we discuss the validity of the Feynman path integral description of the heat kernel for D=11 supermembranes and obtain a matrix Feynman-Kac formula.Comment: 19 pages. AMS LaTeX. A whole new section was added and some other minor changes in style where mad

On BPS bounds in D=4 N=2 gauged supergravity II: general matter couplings and black hole masses

We continue the analysis of BPS bounds started in arXiv:1110.2688, extending it to the full class of N=2 gauged supergravity theories with arbitrary vector and hypermultiplets. We derive the general form of the asymptotic charges for asymptotically flat (M_4), anti-de Sitter (AdS_4), and magnetic anti-de Sitter (mAdS_4) spacetimes. Some particular examples from black hole physics are given to explicitly demonstrate how AdS and mAdS masses differ when solutions with non-trivial scalar profiles are considered.Comment: 21 pages; v2 added reference, published version; v3 minor correction

The Role of Family Functioning in the Association Between Childhood Sexual Victimization and Substance Use in Non-treatment Populations: Results from a Native Canadian Community and Comparisons with the General Population

Using path analytic techniques, this study examines the relationship between childhood sexual victimization and alcohol consumption in adult life, focusing in particular on the role of family functioning and the surrounding social support network of family and friends. Two non-treatment populations are compared, one, an Ontario Native community, and the other, the general Ontario population. The models are estimated separately for males and females. While the results for the two samples differ significantly in certain respects (including by sex), the importance of family functioning as an intervening factor is apparent for both Natives and non-Natives. The results of the path analyses for the two samples suggest that, among the Native group, sexual abuse is significantly and positively related to alcohol consumption through the family dysfunction measure for both males and females and through non-family support for females alone. In the general population sample, conversely, none of the three social support measures tested link sexual abuse to alcohol consumption. Instead, quality of parental relationships appears relatively more important among males in particular in predicting level of family dysfunction and supportive relations with family. These findings provide limited support for the hypothesized mediating influence of the informal support network in the relationship of childhood sexual victimization to substance abuse outcomes; they also point to notable differences for males and females in the dynamics of family life and substance use. The comparability of the Native and non-Native populations with respect to prevalence estimates and implications of the findings for policy are discussed

Determinants of the Risk and Timing of Alcohol and Illicit Drug Use Onset Among Natives and Non-natives: Similarities and Differences

Objective: Employing probability samples from the Ontario Health Survey Supplement (Ontario Ministry of Health, 1990/91) and a community of Native Ontario reserve residents (Embree, 1993), this study compared and contrasted Natives\u27 and Non-natives\u27 determinants of drug and alcohol use onset. Method: Proportional Hazards techniques identified factors associated with the risk and timing of onset of substance use (alcohol and illicit drugs) for both cultural groups, and special attention was paid to the role of family background characteristics as precursors to early alcohol and drug-use onset. Results: The multivariate results reveal that, for both Natives and Non-natives alike, and considering both drinking and drug use onset together, age cohort predominates as a risk factor, with youngest groups at greatest risk, and especially in the case of drug use other than alcohol. Males also exhibit consistently higher risks of both alcohol and other substance use, and this is true to a greater extent for Non-natives. For the model of drug use timing, age of alcohol use onset is the second best predictor for Natives, although its effect is still apparent, albeit weaker, in the case of Non-natives. The results concerning age at first regular drinking lend further support to previous findings that alcohol use is a powerful predisposing factor to the use of illicit substances. However, the evident cultural disparity in the predictive power of this measure also suggests that Natives may lag behind the general population with respect to recently observed shifts in the pattern of substance use progression (i.e., away from alcohol use as a necessary precondition to illicit use of other drugs). As for family characteristics, a number of factors emerge as determinants of risk but appear to depend, at least in part, on the cultural group and the substance under consideration: namely, parental substance abuse, paternal history of depression, quality of parental relations, parental occupational background, and sexual abuse during childhood. Conclusions: Overall, the findings point to the salience of family background in affecting early onset drinking and drug use, behaviors well-recognized to have potentially adverse mental and physical health consequences, as well as negative social outcomes

N=2 Conformal Superspace in Four Dimensions

We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to N=2 our prior result for N=1 superspace. This formulation explicitly lifts to superspace the existing methods of the N=2 superconformal tensor calculus; at the same time the geometry, when degauged to SL(2,C) x U(2)_R, reproduces the existing formulation of N=2 conformal supergravity constructed by Howe.Comment: 43 pages; v2 references added, acknowledgments update