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 spectrum of a Noncommutative Formulation of the D=11 Supermembrane with Winding

A regularized model of the double compactified D=11 supermembrane with nontrivial winding in terms of SU(N) valued maps is obtained. The condition of nontrivial winding is described in terms of a nontrivial line bundle introduced in the formulation of the compactified supermembrane. The multivalued geometrical objects of the model related to the nontrivial wrapping are described in terms of a SU(N) geometrical object which in the $N\to \infty$ limit, converges to the symplectic connection related to the area preserving diffeomorphisms of the recently obtained non-commutative description of the compactified D=11 supermembrane.(I. Martin, J.Ovalle, A. Restuccia. 2000,2001) The SU(N) regularized canonical lagrangian is explicitly obtained. In the $N\to \infty$ limit it converges to the lagrangian in (I.Martin, J.Ovalle, A.Restuccia. 2000,2001) subject to the nontrivial winding condition. The spectrum of the hamiltonian of the double compactified D=11 supermembrane is discussed. Generically, it contains local string like spikes with zero energy. However the sector of the theory corresponding to a principle bundle characterized by the winding number $n \neq 0$, described by the SU(N) model we propose, is shown to have no local string-like spikes and hence the spectrum of this sector should be discrete.Comment: 16 pages.Latex2

Off-shell N=2 tensor supermultiplets

A multiplet calculus is presented for an arbitrary number n of N=2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkahler or quaternion-Kahler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kahler manifolds with two commuting isometries is given.Comment: 36 page

Consistent truncation of d = 11 supergravity on AdS_4 x S^7

We study the system of equations derived twenty five years ago by B. de Wit and the first author [Nucl. Phys. B281 (1987) 211] as conditions for the consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 to gauged N = 8 supergravity in four dimensions. By exploiting the E_7(7) symmetry, we determine the most general solution to this system at each point on the coset space E_7(7)/SU(8). We show that invariants of the general solution are given by the fluxes in eleven-dimensional supergravity. This allows us to both clarify the explicit non-linear ansatze for the fluxes given previously and to fill a gap in the original proof of the consistent truncation. These results are illustrated with several examples.Comment: 41 pages, typos corrected, published versio

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

New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!

An extended class of N=2 locally supersymmetric invariants with higher-derivative couplings based on full superspace integrals, is constructed. These invariants may depend on unrestricted chiral supermultiplets, on vector supermultiplets and on the Weyl supermultiplet. Supersymmetry is realized off-shell. A non-renormalization theorem is proven according to which none of these invariants can contribute to the entropy and electric charges of BPS black holes. Some of these invariants may be relevant for topological string deformations.Comment: 24 pages, v2: version published in JHEP, one reference added and typos corrected, v3: reference adde

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

Electric and magnetic charges in N=2 conformal supergravity theories

General Lagrangians are constructed for N=2 conformal supergravity theories in four space-time dimensions involving gauge groups with abelian and/or non-abelian electric and magnetic charges. The charges are encoded in the gauge group embedding tensor. The scalar potential induced by the gauge interactions is quadratic in this tensor, and, when the embedding tensor is treated as a spurionic quantity, it is formally covariant with respect to electric/magnetic duality. This work establishes a general framework for studying any deformation induced by gauge interactions of matter-coupled N=2 supergravity theories. As an application, full and residual supersymmetry realizations in maximally symmetric space-times are reviewed. Furthermore, a general classification is presented of supersymmetric solutions in $\mathrm{AdS}_2\times S^2$ space-times. As it turns out, these solutions allow either eight or four supersymmetries. With four supersymmetries, the spinorial parameters are Killing spinors of $\mathrm{AdS}_2$ that are constant on $S^2$, so that they carry no spin, while the bosonic background is rotationally invariant.Comment: 49 pages, typos correcte