Simple superamplitudes in higher dimensions

We provide simple superspaces based on a formulation of spinor helicity in general even dimensions. As a distinguishing feature these spaces admit a fermionic super-momentum conserving delta function solution to the on-shell supersymmetry Ward identities. Using these solutions, we present beautifully simple formulae for the complete three, four and five point superamplitudes in maximal super Yang-Mills theory in eight dimensions, and for the three and four point superamplitudes in ten dimensional type IIB supergravity. In addition, we discuss the exceptional kinematics of the three point amplitude, and the supersymmetric spinorial BCFW recursion, in general dimensions.Comment: 34 page

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\tilde\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\mathcal{N}=4$ super-Yang-Mills theory, $\Omega^{(1)}$ and $\Omega^{(2)}$. The derivative of $\Omega^{(2)}$ with respect to one of the conformal invariants yields $\tilde\Phi_6$, while another first-order differential operator applied to $\tilde\Phi_6$ yields $\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\mathcal{N}=4$ super-Yang-Mills.Comment: 18 pages, 2 figure

Yangian symmetry of light-like Wilson loops

We show that a certain class of light-like Wilson loops exhibits a Yangian symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills theory in a certain kinematical regime. The fact that we find a Yangian symmetry constraining their functional form can be thought of as the effect of the original conformal symmetry associated to the scattering amplitudes in the N=4 theory.Comment: 15 pages, 5 figure

Three particle superstring amplitudes with massive legs

On-shell superspaces and associated spinor helicity techniques give an efficient formulation of the Ward identities of on-shell supersymmetry for scattering amplitudes and supply tools to construct their solutions. Based on these techniques in this paper the general solutions of the Ward identities are presented for three particle scattering amplitudes with one, two or three massive legs for simple supersymmetry in ten and eight dimensions. It is shown in examples how these solutions may be used to obtain concrete amplitudes for the closed (IIB) and open superstring in a flat background. Explicit results include all three point amplitudes with one massive leg whose functional form is shown to be dictated completely by super-Poincare symmetry. The resulting surprisingly simple series only involves massive superfields labelled by completely symmetric little group representations. The extension to more general explicit three and higher point amplitudes in string theory is initiated. In appendices the field content of the fundamental massive superfields of the open and closed superstring are listed in terms of the Dynkin labels of a variety of groups which may be of independent interest.Comment: 45 pages. v2: typos corrected, references adde

Willing suspension of disbelief: a study in online learning through simulation, and its potential for deeper learning in Higher Education

This article describes the replacement of a 'traditionally taught' law of probate course (lectures and workshops/tutorials) with an on-line collaborative learning exercise using simulation and role-play which is referred to hereafter as the Transactional Learning Project ('TLP'). The article considers the theory that the emotional engagement that comes about through role play in simulation leads to deeper learning, a process Maharg (2010) has dubbed as the 'integration of the cognitive and the affective'. The article includes statistical analysis of student feedback on the TLP in an attempt to measure how easy it is to carry students predisposed to expect information to be 'given' rather than 'acquired' along the journey leading away from traditional didactic teaching. The project was motivated partly by the dearth of such learning practices on the Legal Practice Course. It is suggested that the findings of the project add to the body of research which tends to illustrate the success in terms of student learning from working in leaderless (i.e. where the tutor is absent from the collaborative group) groups engaged in practical tasks involving simulation

Amplitudes for Multiple M5 Branes

We study N=(m,0) super-Poincare invariant six-dimensional massless and five-dimensional massive on-shell amplitudes. We demonstrate that in six dimensions, all possible three-point amplitudes involving tensor multiplets are necessarily embedded in gravitational theories. For non-gravitational amplitudes we consider instead five-dimensional massive amplitudes with N=(2,0) supersymmetry, aiming at describing the world volume theory of multiple M5 branes compactified on M^{4,1}x S^1. We find non-gravitational amplitudes whose on-shell degrees of freedom are shown to match those of the massive particle states that arise from self-dual strings wrapping a circle. Along the way we find interesting hints of a fermionic symmetry in the (2,0) theory, which accompanies the self-dual tensor gauge symmetry. We also discuss novel theories with (3,0) and (4,0) supersymmetry.Comment: 49 pages, 4 figures, v2: Better organization and more details in the section on KK interaction

Cultivating reflexive research practice when using participants’ photographs as research data

This chapter reflects on a study exploring the development of a feminist consciousness. During the interviews participants were invited to share photographs that were significant to their feminist becoming. Various ethical and methodological challenges arose through the use of visual data, in particular the ethics of the interpretation and dissemination of participants’ personal photographs. Both issues were highlighted and addressed through reflexive research practice, which exposed how the researcher’s reaction to and feelings about the photographs impacted upon how they were interpreted and shared. Reflexivity demands that researchers interrogate their research choices and is essential for ethical and rigorous research. This chapter argues that visual methods, whilst posing new ethical challenges, can enhance the reflexive research practice necessary for responding to and navigating its challenges

Bootstrapping the three-loop hexagon

We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N=4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3-->3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.Comment: 36 pages, 1 figure, plus 8 ancillary files containing symbols of functions; v2 minor typo correction

Unfitting, uncomfortable, unacademic: a sociological reading of an interactive mobile phone app in university lectures

Abstract Scholarly literature on education technology uptake has been dominated by technological determinist readings of students’ technology use. However, in recent years there has been a move by sociologists of education to highlight how the contexts in which educational technologies are introduced are not tabula rasa but socially and culturally complex. This study approaches technology as a social construct, arguing that students construct discursive meaning of, rather than simply respond to, technologies for learning. The study explores students’ constructions of a mobile learning app that was introduced into lectures during a year-long university course. Students largely rejected the app, constructing it as unfitting for the context, a socially uncomfortable experience and an unacademic way of learning. The paper highlights the limitations of technological determinism and closes by arguing for readings of educational technologies that pay close attention to students’ voices