In the context of string theory, axions appear to provide the most plausible solution of the strong CP problem. However, as has been known for a long time, in many stringbased models, the axion coupling parameter F a is several orders of magnitude higher than the standard cosmological bounds. We re-examine this problem in a variety of models, showing that F a is close to the GUT scale or above in many models that have GUT-like phenomenology, as well as some that do not. On the other hand, in some models with Standard Model gauge fields supported on vanishing cycles, it is possible for F a to be well below the GUT scale.

As an alternative to the usual Feynman graphs, tree amplitudes in Yang-Mills theory can be constructed from tree graphs in which the vertices are tree level MHV scattering amplitudes, continued off shell in a particular fashion. The formalism leads to new and relatively simple formulas for many amplitudes, and can be heuristically derived from twistor space.

In the context of string theory, axions appear to provide the most plausible solution of the strong CP problem. However, as has been known for a long time, in many stringbased models, the axion coupling parameter F a is several orders of magnitude higher than the standard cosmological bounds. We re-examine this problem in a variety of models, showing that F a is close to the GUT scale or above in many models that have GUT-like phenomenology, as well as some that do not. On the other hand, in some models with Standard Model gauge fields supported on vanishing cycles, it is possible for F a to be well below the GUT scale.

We derive general tree-level recursion relations for amplitudes which include massive propagating particles. As an illustration, we apply these recursion relations to scattering amplitudes of gluons coupled to massive scalars. We provide new results for all amplitudes with a pair of scalars and n ≤ 4 gluons. These amplitudes can be used as building blocks in the computation of one-loop 6-gluon amplitudes using unitarity based methods. * On Leave from Princeton University At one loop, the MHV rules have been successfully applied to supersymmetric amplitudes [25][26][27][28][29][30][31]. New classes of amplitudes have been derived with the new methods in Refs. [5,[32][33][34][35][36][37][38][39][40][41][42]. All of these results give complete amplitudes only in supersymmetric theories which are cut-constructible in 4 dimensions [6,7]. In non-supersymmetric gauge theories, the new methods apply only to the 4D cut-constructible parts of the amplitudes.The second motivation of this paper is to assemble together the pieces necessary for the complete calculation of one-loop amplitudes in non-supersymmetric gauge theories.

We show that, in analyzing differential equations obeyed by one-loop gauge theory amplitudes, one must take into account a certain holomorphic anomaly. When this is done, the results are consistent with the simplest twistor-space picture of the available one-loop amplitudes.