New Complete Non-compact Spin(7) Manifolds

We construct new explicit metrics on complete non-compact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by A_8, is topologically R^8 and another, which we denote by B_8, is the bundle of chiral spinors over $S^4$. Unlike the previously-known complete non-compact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S^4, our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP^3. We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of opposite dualities) for the B_8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L^2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A_8 and B_8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In an appendix we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B^+_8 and B^-_8 similar to B_8.Comment: Latex, 29 pages. Appendix obtaining general solution of first-order equations and additional complete Spin(7) manifolds adde

Black Holes and Calogero Models

We argue that the large $n$ limit of the $n$-particle $SU(1,1|2)$ superconformal Calogero model provides a microscopic description of the extreme Reissner-Nordstr{\"o}m black hole in the near-horizon limit.Comment: Revtex 5pp. Revision includes improved discussion of entropy and includes an additional referenc

String and M-theory Deformations of Manifolds with Special Holonomy

The R^4-type corrections to ten and eleven dimensional supergravity required by string and M-theory imply corrections to supersymmetric supergravity compactifications on manifolds of special holonomy, which deform the metric away from the original holonomy. Nevertheless, in many such cases, including Calabi-Yau compactifications of string theory and G_2-compactifications of M-theory, it has been shown that the deformation preserves supersymmetry because of associated corrections to the supersymmetry transformation rules, Here, we consider Spin(7) compactifications in string theory and M-theory, and a class of non-compact SU(5) backgrounds in M-theory. Supersymmetry survives in all these cases too, despite the fact that the original special holonomy is perturbed into general holonomy in each case.Comment: Improved discussion of SU(5) holonomy backgrounds. Other minor typos corrected. Latex with JHEP3.cls, 42 page

A Note on Flux Induced Superpotentials in String Theory

Non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory. Gukov has conjectured the explicit form of this superpotential. We check this conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well as for warped M-theory compactifications on Spin(7) holonomy manifolds, by performing a Kaluza-Klein reduction.Comment: 19 pages, no figure

Horava-Witten Stability: eppur si muove

We construct exact time-dependent solutions of the supergravity equations of motion in which two initially non-singular branes, one with positive and the other with negative tension, move together and annihilate each other in an all-enveloping spacetime singularity. Among our solutions are the Horava-Witten solution of heterotic M-theory and a Randall-Sundrum I type solution, both of which are supersymmetric, i.e. BPS, in the time-independent case. In the absence of branes our solutions are of Kasner type, and the source of instability may ascribed to a failure to stabilise some of the modulus fields of the compactification. It also raises questions about the viability of models based on some sorts of negative tension brane.Comment: Latex, 22 pages, extended discussion of the global spacetime structure, and reference adde

Geometric Aspects of D-branes and T-duality

We explore the differential geometry of T-duality and D-branes. Because D-branes and RR-fields are properly described via K-theory, we discuss the (differential) K-theoretic generalization of T-duality and its application to the coupling of D-branes to RR-fields. This leads to a puzzle involving the transformation of the A-roof genera in the coupling.Comment: 26 pages, JHEP format, uses dcpic.sty; v2: references added, v3: minor change

Supersymmetric Non-singular Fractional D2-branes and NS-NS 2-branes

We obtain regular deformed D2-brane solutions with fractional D2-branes arising as wrapped D4-branes. The space transverse to the D2-brane is a complete Ricci-flat 7-manifold of G_2 holonomy, which is asymptotically conical with principal orbits that are topologically CP^3 or the flag manifold SU(3)/(U(1) x U(1)). We obtain the solution by first constructing an L^2 normalisable harmonic 3-form. We also review a previously-obtained regular deformed D2-brane whose transverse space is a different 7-manifold of G_2 holonomy, with principal orbits that are topologically S^3 x S^3. This describes D2-branes with fractional NS-NS 2-branes coming from the wrapping of 5-branes, which is supported by a non-normalisable harmonic 3-form on the 7-manifold. We prove that both types of solutions are supersymmetric, preserving 1/16 of the maximal supersymmetry and hence that they are dual to {\cal N}=1 three-dimensional gauge theories. In each case, the spectrum for minimally-coupled scalars is discrete, indicating confinement in the infrared region of the dual gauge theories. We examine resolutions of other branes, and obtain necessary conditions for their regularity. The resolution of many of these seems to lie beyond supergravity. In the process of studying these questions, we construct new explicit examples of complete Ricci-flat metrics.Comment: Latex, 30 page

Non-Kaehler attracting manifolds

We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski "attractor points'' for 3-form fluxes are special-hermitian manifolds.Comment: 18 pages. v2: Minor polishing, reference added. v3: More cleanup, final version for JHE

Chiral Supergravity

We study the linearized approximation of N=1 topologically massive supergravity around AdS3. Linearized gravitino fields are explicitly constructed. For appropriate boundary conditions, the conserved charges demonstrate chiral behavior, so that chiral gravity can be consistently extended to chiral supergravity.Comment: 30 page

Turning to God in the Face of Ostracism: Effects of Social Exclusion on Religiousness

The present research proposes that individuals who are socially excluded can turn to religion to cope with the experience. Empirical studies conducted to test this hypothesis consistently found that socially excluded persons reported (a) significantly higher levels of religious affiliation (Studies 1, 2, and 4) and (b) stronger intentions to engage in religious behaviors (Study 2) than comparable, nonexcluded individuals. Direct support for the stress-buffering function of religiousness was also found, with a religious prime reducing the aggression-eliciting effects of consequent social rejection (Study 5). These effects were observed in both Christian and Muslim samples, revealing that turning to religion can be a powerful coping response when dealing with social rejection. Theoretical and practical implications of these findings are discussed