Perturbative expansion of N<8 Supergravity

We characterise the one-loop amplitudes for N=6 and N=4 supergravity in four dimensions. For N=6 we find that the one-loop n-point amplitudes can be expanded in terms of scalar box and triangle functions only. This simplification is consistent with a loop momentum power count of n-3, which we would interpret as being n+4 for gravity with a further -7 from the N=6 superalgebra. For N=4 we find that the amplitude is consistent with a loop momentum power count of n, which we would interpret as being n+4 for gravity with a further -4 from the N=4 superalgebra. Specifically the N=4 amplitudes contain non-cut-constructible rational terms.Comment: 13 pages. v2 adds analytic expression for rational parts of 5-pt 1-loop N=4 SUGRA amplitude; v3 normalisations clarifie

Dietary resource utilization patterns and head morphology among three sympatric watersnake species.

The coexistence of similar species may be related to a variety of resource utilization differences. Dietary resource utilization variation may be the most important difference allowing for the coexistence of sympatric snake species. Many watersnakes (Nerodia spp.) live in sympatry and use similar aquatic habitats feeding on similar prey. While these sympatric watersnakes may have different general foraging patterns, snake diet may be affected by a variety of factors. Therefore, I initiated an investigation to understand the coexistence of sympatric plain-bellied (N. erythrogaster), diamondback (N. rhombifer) and northern (N. sipedon) watersnakes by addressing their dietary resource utilization patterns. Results indicated that northern watersnakes ate fish families according to their availability except for the avoidance of Aphredoderidae. I also determined that northern watersnakes had smaller head sizes and a diet closer to the piscivorous diamondback watersnake. There were sex differences in snake head size and all three species had different head shapes relating to diet. In addition, gut contents were determined with plain-bellieds feeding mainly on anurans, diamondbacks on fishes, and northern watersnakes feeding mostly on fishes but with a higher anuran component than diamondback watersnakes. Stable isotope analyses provided long-term dietary information with diamondback watersnakes feeding at higher trophic levels while plain-bellied watersnakes fed more from terrestrial prey sources. The application of stable isotope techniques helped to demonstrate shifts in dietary resource utilization. This research has allowed me to reveal a complex foraging system affected by a variety of factors allowing for the coexistence of sympatric watersnakes

Obtaining One-loop Gravity Amplitudes Using Spurious Singularities

The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations create a web of interactions between the various terms. We explore the extent to which entire one-loop amplitudes can be determined from these relationships starting with a relatively small input of initial information, typically the coefficients of the scalar integral functions as these are readily determined. In the context of one-loop gravity amplitudes, of which relatively little is known, we find that some amplitudes with a small number of legs can be completely determined from their box coefficients. For increasing numbers of legs, ambiguities appear which can be determined from the physical singularity structure of the amplitude. We illustrate this with the four-point and N=1,4 five-point (super)gravity one-loop amplitudes.Comment: Minor corrections. Appendix adde

Baryon Number Violating Transitions in String Backgrounds

We construct field configurations that interpolate between string background states of differing baryon number. Using these configurations we estimate the effect of the background fields on the energy barrier separating different vacua. In the background of a superconducting GUT string the energy barrier is increased, while in an electroweak string background or the electroweak layer of a non-superconducting string the energy barrier is reduced. The energy barrier depends sensitively on both the background gauge and scalar fields.Comment: 27 pages. Texing problems fixe

Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos

We show how Supersymmetric Ward identities can be used to obtain amplitudes involving gluinos or adjoint scalars from purely gluonic amplitudes. We obtain results for all one-loop six-point NMHV amplitudes in \NeqFour Super Yang-Mills theory which involve two gluinos or two scalar particles. More general cases are also discussed.Comment: 32 pages, minor typos fixed; one reference adde

The n-point MHV one-loop Amplitude in N=4 Supergravity

We present an explicit formula for the n-point MHV one-loop amplitude in a N=4 supergravity theory. This formula is derived from the soft and collinear factorisations of the amplitude.Comment: 8 pages; v2 References added. Minor changes to tex

Stability of an electroweak string with a fermion condensate

A solution of the standard electroweak theory with a single lepton family is constructed, consisting of a cosmic string and a fermion condensate within its core. The stability of this system to small perturbations is examined, and it is found that stability is not enhanced relative to the bare electroweak string. The presence of quark zero modes is shown to violate the existence criteria for embedded defects.Comment: 13 pages, preprint DAMTP 94-9, SWAT/2