Supergravities with positive definite potentials and AdS pp-waves

Ten-dimensional superstring theory (or the conjectured nonperturbative Mtheory in eleven dimensions) is the most promising candidate for a consistent quantum theory of gravity capable of unifying all known forces of nature. An important question concerning these fundamental theories is how they compactify to lower dimensions and how to obtain a real four dimensional world? In this dissertation we present new avenues for M/string theory to reduce to lower dimensions as well as to four dimensions. For example, we show that by performing a generalized Kaluza-Klein IR reduction on the low-energy field theory of the heterotic string, the resulting lower dimensional theory compactifies spontaneously on S3 to give rise to (Minkowski)6 spacetime. Furthermore, a generalized reduction of M-theory on K3 à IR compacti- fies spontaneously on S2 to give rise to a (Minkowski)4 spacetime. The generalized Kaluza-Klein reduction gauges the Cremmer-Julia type global symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion by giving the higher dimensional fields an additional dependence on the circle coordinate. We apply the generalized reduction scheme to half-maximal supergravities which are obtained from the heterotic string (or the NS-NS sector of the type-II string) compactified on a (10 − D)-dimensional torus truncated to the pure supergravity multiplet. This gives rise to new gauged supergravities in diverse dimensions with supersymmetric Minkowski à sphere vacua.Since two large extra dimensions have received much attention recently, we make a detailed study of the gauged D = 6, N = (1, 1) supergravity. In particular, we show that this theory allows for a consistent sphere reduction on S2 to give rise to D = 4, N = 2 supergravity coupled to a vector multiplet which can further be truncated to N = 1 supergravity with a chiral multiplet. We also investigate pp-waves in AdS backgrounds, i.e. pp-waves as solutions of gauged supergravities with AdS vacua. These solutions generically preserve 1 4 of the supersymmetry. We demonstrate supernumerary supersymmetries for both purely gravitational pp-waves and pp-waves supported by fields strengths. These new backgrounds provide interesting novel features of the supersymmetry enhancement for the dual conformal field theory in the infinite-momentum frame

Supergravities with positive definite potentials and AdS pp-waves

Ten-dimensional superstring theory (or the conjectured nonperturbative Mtheory in eleven dimensions) is the most promising candidate for a consistent quantum theory of gravity capable of unifying all known forces of nature. An important question concerning these fundamental theories is how they compactify to lower dimensions and how to obtain a real four dimensional world? In this dissertation we present new avenues for M/string theory to reduce to lower dimensions as well as to four dimensions. For example, we show that by performing a generalized Kaluza-Klein IR reduction on the low-energy field theory of the heterotic string, the resulting lower dimensional theory compactifies spontaneously on S3 to give rise to (Minkowski)6 spacetime. Furthermore, a generalized reduction of M-theory on K3 à IR compacti- fies spontaneously on S2 to give rise to a (Minkowski)4 spacetime. The generalized Kaluza-Klein reduction gauges the Cremmer-Julia type global symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion by giving the higher dimensional fields an additional dependence on the circle coordinate. We apply the generalized reduction scheme to half-maximal supergravities which are obtained from the heterotic string (or the NS-NS sector of the type-II string) compactified on a (10 − D)-dimensional torus truncated to the pure supergravity multiplet. This gives rise to new gauged supergravities in diverse dimensions with supersymmetric Minkowski à sphere vacua.Since two large extra dimensions have received much attention recently, we make a detailed study of the gauged D = 6, N = (1, 1) supergravity. In particular, we show that this theory allows for a consistent sphere reduction on S2 to give rise to D = 4, N = 2 supergravity coupled to a vector multiplet which can further be truncated to N = 1 supergravity with a chiral multiplet. We also investigate pp-waves in AdS backgrounds, i.e. pp-waves as solutions of gauged supergravities with AdS vacua. These solutions generically preserve 1 4 of the supersymmetry. We demonstrate supernumerary supersymmetries for both purely gravitational pp-waves and pp-waves supported by fields strengths. These new backgrounds provide interesting novel features of the supersymmetry enhancement for the dual conformal field theory in the infinite-momentum frame

AdS pp-waves

We obtain the pp-waves of D=5 and D=4 gauged supergravities supported by $U(1)^3$ and $U(1)^4$ gauge field strengths respectively. We show that generically these solutions preserve 1/4 of the supersymmetry, but supernumerary supersymmetry can arise for appropriately constrained harmonic functions associated with the pp-waves. In particular it implies that the solutions are independent of the light-cone coordinate $x^+$. We also obtain the pp-waves in the Freedman-Schwarz model.Comment: Latex, 19 pages, minor changes, to appear in JHE

Contributions of TetrUSS to Project Orion

The NASA Constellation program has relied heavily on Computational Fluid Dynamics simulations for generating aerodynamic databases and design loads. The Orion Project focuses on the Orion Crew Module and the Orion Launch Abort Vehicle. NASA TetrUSS codes (GridTool/VGRID/USM3D) have been applied in a supporting role to the Crew Exploration Vehicle Aerosciences Project for investigating various aerodynamic sensitivities and supplementing the aerodynamic database. This paper provides an overview of the contributions from the TetrUSS team to the Project Orion Crew Module and Launch Abort Vehicle aerodynamics, along with selected examples to highlight the challenges encountered along the way. A brief description of geometries and tasks will be discussed followed by a description of the flow solution process that produced production level computational solutions. Four tasks conducted by the USM3D team will be discussed to show how USM3D provided aerodynamic data for inclusion in the Orion aero-database, contributed data for the build-up of aerodynamic uncertainties for the aero-database, and provided insight into the flow features about the Crew Module and the Launch Abort Vehicle