A note on compactifications on spin(7)-holonomy manifolds

In this note we consider compactifications of Script M-theory on Spin(7)-holonomy manifolds to three-dimensional Minkowski space. In these compactifications a warp factor is included. The conditions for unbroken N = 1 supersymmetry give rise to determining equations for the 4-form field strength in terms of the warp factor and the self-dual 4-form of the internal manifold

Graviton scattering amplitudes in M theory

We compute graviton scattering amplitudes in M theory using Feynman rules for a scalar particle coupled to gravity in eleven dimensions. The processes that we consider describe the single graviton exchange and the double graviton exchange, that in M(atrix) theory correspond to the v^4/r^7 and v^6/r^14 term, respectively. We argue that the v^6/r^14 term appearing in M(atrix) theory at two loops can be obtained from the covariant eleven-dimensional four-graviton amplitude. Finally, we calculate the v^8/r^18 term appearing at two loops in M(atrix) theory. It has been previously conjectured that this term is related to a four graviton scattering amplitude involving the R^4 vertex of M theory

Supersymmetry Breaking, M-Theory and Fluxes

We consider warped compactifications of ${\cal M}$-theory to three-dimensional Minkowski space on compact eight-manifolds. Taking all the leading quantum gravity corrections of eleven-dimensional supergravity into account we obtain the solution to the equations of motion and Bianchi identities. Generically these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant.Comment: 17 pages, TEX, no figures. References adde

Complete Solution for M(atrix) Theory at Two Loops

The complete result for the effective potential for two graviton exchange at two loops in M(atrix) theory can be expressed in terms of a generalized hypergeometric function.Comment: 4 pages, TeX, no figure

Compactifying M-Theory to Four Dimensions

We consider compactifications of ${\cal M}$-theory to four-dimensional Minkowski space on seven-dimensional non-compact manifolds. These compactifications include a warp factor which is non-constant due to the presence of sources coming from fivebranes wrapping two-dimensional submanifolds of the internal seven-dimensional space. We derive the expression for the field strengths and consider an explicit example of this general class of solutions.Comment: 15 pages, TeX, no figures, references adde

Runaway in the Landscape

We consider flux compactifications of type IIB string theory on the mirror of a rigid Calabi-Yau. In special cases, these models are dual to the type IIA flux vacua with runaway direction in flux space. We show that new weak coupling AdS solutions can be found for large complex structure, while Minkowski solutions with all moduli stabilized are confined to be at strong coupling. The existence of these solutions, as found in a previous work, is nevertheless guaranteed by a non-renormalization theorem of the type IIB flux superpotential. Based on our results, we are led to the conjecture that supersymmetric runaway directions in flux space are always accompanied by a spectrum of moduli masses reaching down to the AdS scale. This could be violated in a non-supersymmetric situation.Comment: 26 page

String Corrected Spacetimes and SU(N)-Structure Manifolds

Using an effective field theory approach and the language of SU(N)-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that the internal geometry remains flat and uncorrected. For n=4, 6, Kahler manifolds with SU(N)-holonomy can become corrected to SU(N)-structure, while preserving supersymmetry, once corrections are included.Comment: 27 page

Fivebranes, Membranes and Non-Perturbative String Theory

Non-perturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order $e^{-1/g_s}$ contributions, where $g_s$ is the string coupling. The computation reduces to a weighted sum of supersymmetric extremal maps of strings, membranes and fivebranes into the Calabi-Yau space, all three of which enter on equal footing. It is shown that a supersymmetric 3-cycle is one for which the pullback of the K\"ahler form vanishes and the pullback of the holomorphic three-form is a constant multiple of the volume element. Quantum mirror symmetry relates the sum in the IIA theory over supersymmetric, odd-dimensional cycles in the Calabi-Yau space to a sum in the IIB theory over supersymmetric, even-dimensional cycles in the mirror.Comment: 34 pages, phyzzx (A new section about conifold singularities in hypermultiplet moduli spaces is added