SU(3)-instantons and G2,Spin(7)G_2, Spin(7)-heterotic string solitons

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimensions 6. Non-conformally flat non-compact solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 7 and 8. A Riemannian metric with holonomy contained in $G_2$ arises from our considerations and Hitchin's flow equations, which seems to be new. Compact examples of $SU(3), G_2$ and $Spin(7)$ instanton satisfying the anomaly cancellation conditions are presented.Comment: LaTex, 22 pages, Corrected anomaly cancellation, final version to appear in Commun. Math. Phy

Axisymmetric non-abelian BPS monopoles from G_2 metrics

Exact $SU(2)\times U(1)$ self-gravitating BPS global monopoles in four dimensions are constructed by dimensional reduction of eight dimensional metrics with $G_2$ holonomy asymptotic to cones over $S^3\times S^3$. The solutions carry two topological charges in an interesting way. They are generically axially but not spherically symmetric. This last fact is related to the isometries and asymptotic topology of the $G_2$ metrics. It is further shown that some $G_2$ metrics known numerically reduce to supersymmetric cosmic strings.Comment: Latex. 1+21 pages. References update

Orientifolds and Slumps in G_2 and Spin(7) Metrics

We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which are complete on a complex line bundle over CP^3. The principal orbits are S^7, described as a triaxially squashed S^3 bundle over S^4. The behaviour in the S^3 directions is similar to that in the Atiyah-Hitchin metric, and we show how this leads to an M-theory interpretation with orientifold D6-branes wrapped over S^4. We then consider new G_2 metrics which we denote by C_7, which are complete on an R^2 bundle over T^{1,1}, with principal orbits that are S^3\times S^3. We study the C_7 metrics using numerical methods, and we find that they have the remarkable property of admitting a U(1) Killing vector whose length is nowhere zero or infinite. This allows one to make an everywhere non-singular reduction of an M-theory solution to give a solution of the type IIA theory. The solution has two non-trivial S^2 cycles, and both carry magnetic charge with respect to the R-R vector field. We also discuss some four-dimensional hyper-Kahler metrics described recently by Cherkis and Kapustin, following earlier work by Kronheimer. We show that in certain cases these metrics, whose explicit form is known only asymptotically, can be related to metrics characterised by solutions of the su(\infty) Toda equation, which can provide a way of studying their interior structure.Comment: Latex, 45 pages; minor correction

Integrable reductions of Spin(7) and G_2 invariant self-dual Yang-Mills equations and gravity

There is remarkable relation between self-dual Yang-Mills and self-dual Einstein gravity in four Euclidean dimensions. Motivated by this we investigate the Spin(7) and G_2 invariant self-dual Yang-Mills equations in eight and seven Euclidean dimensions and search for their possible analogs in gravitational theories. The reduction of the self-dual Yang-Mills equations to one dimension results into systems of first order differential equations. In particular, the Spin(7)-invariant case gives rise to a 7-dimensional system which is completely integrable. The different solutions are classified in terms of algebraic curves and are characterized by the genus of the associated Riemann surfaces. Remarkably, this system arises also in the construction of solutions in gauged supergravities that have an interpretation as continuous distributions of branes in string and M-theory. For the G_2 invariant case we perform two distinct reductions, both giving rise to 6-dimensional systems. The first reduction, which is a complex generalization of the 3-dimensional Euler spinning top system, preserves an SU(2) X SU(2) X Z_2 symmetry and is fully integrable in the particular case where an extra U(1) symmetry exists. The second reduction we employ, generalizes the Halphen system familiar from the dynamics of monopoles. Finally, we analyze massive generalizations and present solitonic solutions interpolating between different degenerate vacua.Comment: 31 pages, latex; v2: some references adde

Analyses showing how religiosity, social activities, and drug-related beliefs mediate relationships between post-high school experiences and substance use

https://deepblue.lib.umich.edu/bitstream/2027.42/137877/1/occ50.pd

Inconsistency of interacting, multi-graviton theories

We investigate, in any spacetime dimension >=3, the problem of consistent couplings for a finite collection of massless, spin-2 fields described, in the free limit, by a sum of Pauli-Fierz actions. We show that there is no consistent (ghost-free) coupling, with at most two derivatives of the fields, that can mix the various "gravitons". In other words, there are no Yang-Mills-like spin-2 theories. The only possible deformations are given by a sum of individual Einstein-Hilbert actions. The impossibility of cross-couplings subsists in the presence of scalar matter. Our approach is based on the BRST-based deformation point of view and uses results on the so-called "characteristic cohomology" for massless spin-2 fields which are explained in detail.Comment: 44+1 pages, no figures. Case of an infinite number of gravitons treated more completely, comparison with work by Aragone and Deser on gravitational coupling of a single massless spin-2 field discusse

RG flows from Spin(7), CY 4-fold and HK manifolds to AdS, Penrose limits and pp waves

We obtain explicit realizations of holographic renormalization group (RG) flows from M-theory, from E^{2,1} \times Spin(7) at UV to AdS_4 \times \tilde{S^7} (squashed S^7) at IR, from E^{2,1} \times CY4 at UV to AdS_4 \times Q^{1,1,1} at IR, and from E^{2,1} \times HK (hyperKahler) at UV to AdS_4 \times N^{0,1,0} at IR. The dual type IIA string theory configurations correspond to D2-D6 brane systems where D6 branes wrap supersymmetric four-cycles. We also study the Penrose limits and obtain the pp-wave backgrounds for the above configurations. Besides, we study some examples of non-supersymmetric and supersymmetric flows in five-dimensional gauge theories.Comment: 42 pages, 6 eps figures, typos and misprints correcte

Gauge/String Duality in Confining Theories

This is the content of a set of lectures given at the XIII Jorge Andre Swieca Summer School on Particles and Fields, held in Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity.Comment: 70 pages, 8 figures, Lectures given at XIII Jorge Andre Swieca Summer School on Particle and Fields, Campos do Jordao, Brazil, January 2005; v2: several explanations were expanded and improved while an oversight, some typos and the list of references were corrected; v3: minor amendments and a few references added; v4: citations added, final versio

Domain walls of N=2 supergravity in five dimensions from hypermultiplet moduli spaces

We study domain wall solutions in d=5, N=2 supergravity coupled to a single hypermultiplet whose moduli space is described by certain inhomogeneous, toric ESD manifolds constructed recently by Calderbank and Singer. Upon gauging a generic U(1) isometry of these spaces, we obtain an infinite family of models whose "superpotential" admits an arbitrary number of isolated critical points. By investigating the associated supersymmetric flows, we prove the existence of domain walls of Randall-Sundrum type for each member of our family, and find chains of domain walls interpolating between various AdS_5 backgrounds. Our models are described by a discrete infinity of smooth and complete one-hypermultiplet moduli spaces, which live on an open subset of the minimal resolution of certain cyclic quotient singularities. These spaces generalize the Pedersen metrics considered recently by Behrndt and Dall' Agata.Comment: 39 pages, numerous figures; v4: two references adde

Modeling the effect of age in T1-2 breast cancer using the SEER database

BACKGROUND: Modeling the relationship between age and mortality for breast cancer patients may have important prognostic and therapeutic implications. METHODS: Data from 9 registries of the Surveillance, Epidemiology, and End Results Program (SEER) of the United States were used. This study employed proportional hazards to model mortality in women with T1-2 breast cancers. The residuals of the model were used to examine the effect of age on mortality. This procedure was applied to node-negative (N0) and node-positive (N+) patients. All causes mortality and breast cancer specific mortality were evaluated. RESULTS: The relationship between age and mortality is biphasic. For both N0 and N+ patients among the T1-2 group, the analysis suggested two age components. One component is linear and corresponds to a natural increase of mortality with each year of age. The other component is quasi-quadratic and is centered around age 50. This component contributes to an increased risk of mortality as age increases beyond 50. It suggests a hormonally related process: the farther from menopause in either direction, the more prognosis is adversely influenced by the quasi-quadratic component. There is a complex relationship between hormone receptor status and other prognostic factors, like age. CONCLUSION: The present analysis confirms the findings of many epidemiological and clinical trials that the relationship between age and mortality is biphasic. Compared with older patients, young women experience an abnormally high risk of death. Among elderly patients, the risk of death from breast cancer does not decrease with increasing age. These facts are important in the discussion of options for adjuvant treatment with breast cancer patients