Nonperturbative Solution of the Super-Virasoro Constraints

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the nonperturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.Comment: 12 pages, CERN-TH.6761/9

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

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

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