The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity

This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D^2k R^4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide powerful constraints on the effective interactions. In the ten-dimensional IIA limit we find that there can be no perturbative contributions beyond k string loops (for k>0). Furthermore, the genus h=k contributions are determined exactly by the one-loop eleven-dimensional supergravity amplitude for all values of k. A plausible interpretation of these observations is that the sum of h-loop Feynman diagrams of maximally extended supergravity is less divergent than might be expected and could be ultraviolet finite in dimensions d < 4 + 6/h -- the same bound as for N=4 Yang--Mills.Comment: 30 pages, 4 figures. v3 Some rewording, typos corrected and some references added. v4: Abstract rephrased. More typos corrected. Version to be publishe

Covariant Matrix Model of Superparticle in the Pure Spinor Formalism

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under $SO(1,10)$ Lorentz group. We first construct a bosonic M(atrix) theory by starting with the first-order formalism of bosonic membrane, which precisely gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this method to the construction of M(atrix) theory of supermembranes. However, it seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory from the Berkovits pure spinor formalism of supermembrane because of the matrix character of the BRST symmetry. Instead, in this paper, we construct a supersymmetric and covariant matrix model of 11D superparticle, which corresponds to a particle limit of covariant M(atrix) theory. By an explicit calculation, we show that the one-loop effective potential is trivial, thereby implying that this matrix model is a free theory at least at the one-loop level.Comment: 13 pages, no figures, two references adde

Supersymmetry Constraints on Type IIB Supergravity

Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.Comment: 31 pages, harvmac (b); minor correction

Anisotropic higher derivative gravity and inflationary universe

Stability analysis of the Kantowski-Sachs type universe in pure higher derivative gravity theory is studied in details. The non-redundant generalized Friedmann equation of the system is derived by introducing a reduced one dimensional generalized KS type action. This method greatly reduces the labor in deriving field equations of any complicate models. Existence and stability of inflationary solution in the presence of higher derivative terms are also studied in details. Implications to the choice of physical theories are discussed in details in this paper.Comment: 9 page

Simulation of the Aerodynamic Interaction between Rotor and Ground Obstacle Using Vortex Method

The mutual aerodynamic interaction between rotor wake and surrounding obstacles is complex, and generates high compensatory workload for pilots, degradation of the handling qualities, and performance, and unsteady force on the structure of the obstacles. The interaction also affects the minimum distance between rotorcrafts and obstacles to operate safely. A vortex-based approach is then employed to investigate the complex aerodynamic interaction between rotors and ground obstacle, and identify the distance where the interaction ends, and this is also the objective of the GARTEUR AG22 working group activities. In this approach, the aerodynamic loads of the rotor blades are described through a panel method, and the unsteady behaviour of the rotor wake is modelled using a vortex particle method. The effects of the ground plane and obstacle are accounted for via a viscous boundary model. The method is then applied to a “Large” and a “Wee” rotor near the ground and obstacle, and compared with the earlier experiments carried out at the University of Glasgow. The results show that predicted rotor induced inflow and flow field compare reasonably well with the experiments. Furthermore, at certain conditions, the tip vortices are pushed up and re-injected into the rotor wake due to the effect of the obstacle resulting in a recirculation. Moreover, contrary to without the obstacle case, peak and thickness of the radial outwash near the obstacle are smaller due to the barrier effect of the obstacle, and an upwash is observed. In addition, as the rotor closes to the obstacle, the rotor slipstreams impinge directly on the obstacle, and the upwash near the obstacle is faster, indicating a stronger interaction between the rotor wake and the obstacle. In addition, contrary to the case without the obstacle, the fluctuations of the rotor thrust, and rolling and pitching moments are obviously strengthened. When the distance between the rotor and the obstacle is larger than 3R, the effect of the obstacle is small

Maximum temperature for an Ideal Gas of U^(1)\hat U(1) Kac-Moody Fermions

A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody fermions. The canonical partition function for the $\hat U(1)$ case is shown to have a maximum temperature $kT_{M} = |\lambda| /\pi$, where $\lambda$ is the coupling of the super charge operator $G_0$ to the fermions. This result is similar to the case of strings but unlike strings the result is obtained from a well-defined lagrangian.Comment: Needs subeqnarray.sty; To be published in Phys. Rev. D, Dec 15, 1995. Some typographical errors have been corrected in the revised versio

The Standard Model on a D-brane

We present a consistent string theory model which reproduces the Standard Model, consisting of a D3-brane at a simple orbifold singularity. We study some simple features of the phenomenology of the model. We find that the scale of stringy physics must be in the multi-TeV range. There are natural hierarchies in the fermion spectrum and there are several possible experimental signatures of the model.Comment: 8 pages Latex, 1 fig. v2: discussion improved, added new reference

D-instanton partition functions

Duality arguments are used to determine D-instanton contributions to certain effective interaction terms of type II supergravity theories in various dimensions. This leads to exact expressions for the partition functions of the finite N D-instanton matrix model in d=4 and 6 dimensions that generalize our previous expression for the case d=10. These results are consistent with the fact that the Witten index of the T-dual D-particle process should only be non-vanishing for d=10.Comment: 20 pages, harvmac, typos corrected, reference adde