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

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

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

Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation

Soft and collinear factorisations can be used to construct expressions for amplitudes in theories of gravity. We generalise the "half-soft" functions used previously to "soft-lifting" functions and use these to generate tree and one-loop amplitudes. In particular we construct expressions for MHV tree amplitudes and the rational terms in one-loop amplitudes in the specific context of N=4 supergravity. To completely determine the rational terms collinear factorisation must also be used. The rational terms for N=4 have a remarkable diagrammatic interpretation as arising from algebraic link diagrams.Comment: 18 pages, axodraw, Proof of eq. 4.3 adde

Regeneration of myelin sheaths of normal length and thickness in the zebrafish CNS correlates with growth of axons in caliber

Demyelination is observed in numerous diseases of the central nervous system, including multiple sclerosis (MS). However, the endogenous regenerative process of remyelination can replace myelin lost in disease, and in various animal models. Unfortunately, the process of remyelination often fails, particularly with ageing. Even when remyelination occurs, it is characterised by the regeneration of myelin sheaths that are abnormally thin and short. This imperfect remyelination is likely to have implications for the restoration of normal circuit function and possibly the optimal metabolic support of axons. Here we describe a larval zebrafish model of demyelination and remyelination. We employ a drug-inducible cell ablation system with which we can consistently ablate 2/3rds of oligodendrocytes in the larval zebrafish spinal cord. This leads to a concomitant demyelination of 2/3rds of axons in the spinal cord, and an innate immune response over the same time period. We find restoration of the normal number of oligodendrocytes and robust remyelination approximately two weeks after induction of cell ablation, whereby myelinated axon number is restored to control levels. Remarkably, we find that myelin sheaths of normal length and thickness are regenerated during this time. Interestingly, we find that axons grow significantly in caliber during this period of remyelination. This suggests the possibility that the active growth of axons may stimulate the regeneration of myelin sheaths of normal dimensions

The MHV QCD Lagrangian

We perform a canonical change of the field variables of light-cone gauge massless QCD to obtain a lagrangian whose terms are proportional up to polarisation factors to MHV amplitudes and continued off shell by the CSW prescription. We solve for this transformation as a series expansion to all orders in the new fields, and use this to prove that the resulting vertices are indeed MHV vertices as claimed. We also demonstrate how this works explicitly for the vertices with: two quarks and two gluons, four quarks, and a particular helicity configuration of two quarks and three gluons. Finally, we generalise the construction to massive QCD