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Cambridge, United Kingdom

Bjornsson J.,Wilberforce Road
Journal of High Energy Physics

This paper provides a more detailed background concerning the previously obtained properties of multi-loop amplitudes in a pure spinor formulation of field theories with maximal supersymmetry. This involves the development of a first quantised field theory version of the non-minimal pure spinor formalism originally designed for describing superstring amplitudes. In addition to superspace world-line fields, the formalism involves a set of world-line ghost fields that are required for implementing BRST invariance with a composite b ghost. In particular, we show that BRST invariance requires the presence of certain contact terms. For four-point amplitudes, these are important beyond two loops. We also present an alternative proof of the "no-triangle hypothesis" and the vanishing of amplitudes with fewer than four external particles. © SISSA 2011. Source

Mason L.,Mathematical Institute andrew Wiles Building | Skinner D.,Wilberforce Road
Journal of High Energy Physics

We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space-time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree-level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories. © 2014 The Author(s). Source

Casali E.,Wilberforce Road
Journal of High Energy Physics

In this short note I show that the soft limit for colour-ordered tree-level YangMills amplitudes contains a sub-leading divergent term. This term is analogous to those found recently by Cachazo and Strominger for tree-level gravity amplitudes. © 2014 The Author(s). Source

Osborn H.,Wilberforce Road | Stergiou A.,Yale University
Journal of High Energy Physics

Abstract: The tensors which may be defined on the conformal manifold for six dimensional CFTs with exactly marginal operators are analysed by considering the response to a Weyl rescaling of the metric in the presence of local couplings. It is shown that there are three symmetric two index tensors only one of which satisfies any positivity conditions. The general results are specialised to the six dimensional conformal theory defined by free two-forms and also to the interacting scalar ϕ3 theory at two loops which preserves conformal invariance to this order. All three two index tensor contributions are present. © 2015, The Author(s). Source

Osborn H.,Wilberforce Road
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Conformal blocks for the finite dimension conformal group SO(2,2) for four point functions for fields with arbitrary spins in two dimensions are obtained by evaluating an appropriate integral. The results are just products of hypergeometric functions of the conformally invariant cross ratios formed from the four complex coordinates. Results for scalars previously obtained are a special case. Applications to four point functions involving the energy momentum tensor are discussed. © 2012 Elsevier B.V. Source

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