arXiv subjects

David Skinner

Publications and source records attributed to David Skinner.

47 records · Page 3Linked to original sources

arXiv2009

Twistor-Strings, Grassmannians and Leading Singularities

We derive a systematic procedure for obtaining an explicit, L-loop leading singularities of planar N=4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum space channel diagrams. The expressions are given as integrals over the moduli of connected, nodal curves in twistor space whose degree and genus matches expectations from twistor-string theory. We propose that a twistor-string theory for pure N=4 super Yang-Mills, if it exists, is determined by the condition that these leading singularity formulae arise as residues when an unphysical contour for the path integral is used, by analogy with the momentum space leading singularity conjecture. We go on to show that the genus g twistor-string moduli space for g-loop N^{k-2}MHV amplitudes may be mapped into the Grassmannian G(k,n). Restricting to a leading singularity, the image of this map is a 2(n-2)-dimensional subcycle of G(k,n) of exactly the type found from the Grassmannian residue formula of Arkani-Hamed, Cachazo, Cheung and Kaplan. Based on this correspondence and the Grassmannian conjecture, we deduce restrictions on the possible leading singularities of multi-loop N^pMHV amplitudes. In particular, we argue that no new leading singularities can arise beyond 3p loops.

hep-th↗

arXiv2009

Scattering Amplitudes and BCFW Recursion in Twistor Space

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for $n$-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N^2MHV super-amplitude. We also give simple closed form formulae for the N=8 supergravity recursion and the MHV and conjugate MHV amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N^kMHV, the amplitudes are given by 2n-4 integrals in the form of Hilbert transforms of a product of $n-k-2$ purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in N=4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.

hep-th↗

arXiv2009

Gravity, Twistors and the MHV Formalism

We give a self-contained derivation of the MHV amplitudes for gravity and use the associated twistor generating function to define a twistor action for the MHV diagram approach to gravity. Starting from a background field calculation on a spacetime with anti self-dual curvature, we obtain a simple spacetime formula for the scattering of a single, positive helicity linearized graviton into one of negative helicity. Re-expressing our integral in terms of twistor data allows us to consider a spacetime that is asymptotic to a superposition of plane waves. Expanding these out perturbatively yields the gravitational MHV amplitudes of Berends, Giele & Kuijf. We go on to take the twistor generating function off-shell at the perturbative level. Combining this with a twistor action for the anti self-dual background, we obtain a twistor action for the MHV diagram approach to perturbative gravity. We finish by extending these results to supergravity, in particular N=4 and N=8.

hep-th↗

arXiv2009

Dual Superconformal Invariance, Momentum Twistors and Grassmannians

Dual superconformal invariance has recently emerged as a hidden symmetry of planar scattering amplitudes in N=4 super Yang-Mills theory. This symmetry can be made manifest by expressing amplitudes in terms of `momentum twistors', as opposed to the usual twistors that make the ordinary superconformal properties manifest. The relation between momentum twistors and on-shell momenta is algebraic, so the translation procedure does not rely on any choice of space-time signature. We show that tree amplitudes and box coefficients are succinctly generated by integration of holomorphic delta-functions in momentum twistors over cycles in a Grassmannian. This is analogous to, although distinct from, recent results obtained by Arkani-Hamed et al. in ordinary twistor space. We also make contact with Hodges' polyhedral representation of NMHV amplitudes in momentum twistor space.

hep-th↗

arXiv2008

On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity

Exploiting singularities in Feynman integrals to get information about scattering amplitudes has been particularly useful at one-loop in theories where no triangles or bubbles appear. At higher loops the integrals possess subtle singularities. In this paper we give these singularities a physical interpretation and show how they turn tedious computations into purely pictorial manipulations. We illustrate our methods with various examples from the computation of four-particle amplitudes in N=4 super Yang-Mills and N=8 supergravity. Along the way we find clues towards an understanding i) of the rung-rule as a consequence of infra-red singularities, ii) of the non rung-rule integrals included in the basis as corrections to the rung-rule and iii) of the coefficients - including signs - of these two types of contribution. The role of corrections is to cancel unphysical singularities generically present in rung-rule integrals. A further byproduct, coming from the fact such unphysical singularities are located where conformal cross-ratios become unity, is the possibility of understanding the dual conformal invariance ansatz for constructing the basis of four-particle amplitudes in N=4 super Yang-Mills.

hep-th↗

arXiv2007

Heterotic twistor-string theory

We reformulate twistor-string theory as a heterotic string based on a twisted (0,2) model. The path integral localizes on holomorphic maps, while the (0,2) moduli naturally correspond to the states of N=4 super Yang-Mills and conformal supergravity under the Penrose transform. We show how the standard twistor-string formulae of scattering amplitudes as integrals over the space of curves in supertwistor space may be obtained from our model. The corresponding string field theory gives rise to a twistor action for N=4 conformal supergravity coupled to super Yang-Mills. The model helps to explain how the twistor-strings of Witten and Berkovits are related and clarifies various aspects of each of these models.

hep-th↗

arXiv2007

From Twistor Actions to MHV Diagrams

We show that MHV diagrams are the Feynman diagrams of certain twistor actions for gauge theories in an axial gauge. The gauge symmetry of the twistor action is larger than that on space-time and this allows us to fix a gauge that makes the MHV formalism manifest but which is inaccessible from space-time. The framework is extended to describe matter fields: as an illustration we explicitly construct twistor actions for an adjoint scalar with arbitrary polynomial potential and a fermion in the fundamental representation and show how this leads to additional towers of MHV vertices in the MHV diagram formalism.

hep-th↗

arXiv2006

Supersymmetric Gauge Theories in Twistor Space

We construct a twistor space action for N=4 super Yang-Mills theory and show that it is equivalent to its four dimensional spacetime counterpart at the level of perturbation theory. We compare our partition function to the original twistor-string proposal, showing that although our theory is closely related to string theory, it is free from conformal supergravity. We also provide twistor actions for gauge theories with N<4 supersymmetry, and show how matter multiplets may be coupled to the gauge sector.

hep-th↗

arXiv2003

Inflation and Kahler Stabilization of the Dilaton

The problems of attempting inflationary model-building in a theory containing a dilaton are explained. In particular, I study the shape of the dilaton potential today and during inflation, based on a weakly-coupled heterotic string model where corrections to the Kahler potential are assumed to be responsible for dilaton stabilization. Although no specific model-building is attempted, if the inflationary energy density is related to the scale of gaugino condensation, then the dilaton may be stabilized close enough to today's value that there is no significant change in the GUT scale coupling. This can occur in a very wide range of models, and helps to provide some justification for the standard predictions of the spectral index. I explain how this result can ultimately be traced to the supersymmetry structure of the theory.

hep-th↗

arXiv2002

Five-Dimensional Moving Brane Solutions with Four-Dimensional Limiting Behaviour

Under certain conditions some solutions to five-dimensional heterotic M-theory can be accurately described by the four-dimensional action of the theory - they have a four-dimensional limit. We consider the connection between solutions of four and five-dimensional heterotic M-theory when moving five-branes are present in the bulk. We begin by describing how to raise the known four-dimensional moving brane solutions to obtain approximate solutions to the five-dimensional theory, presenting for the first time the metric template necessary for this procedure. We then present the first solutions to the five-dimensional theory containing moving five-branes. We can then discuss the connection between our new exact five-dimensional solution and the four-dimensional ones. It is shown that our new solution corresponds to a solution with a static brane in four-dimensions. In other words our new solution could not have been identified as containing a moving brane from a purely four-dimensional viewpoint.

hep-th↗

arXiv2001

Brane-World Inflation and the Transition to Standard Cosmology

In the context of a five-dimensional brane-world model motivated from heterotic M-theory, we develop a framework for potential-driven brane-world inflation. Specifically this involves a classification of the various background solutions of (A)dS_5 type, an analysis of five-dimensional slow-roll conditions and a study of how a transition to the flat vacuum state can be realized. It is shown that solutions with bulk potential and both bane potentials positive exist but are always non-separating and have a non-static orbifold. It turns out that, for this class of backgrounds, a transition to the flat vacuum state during inflation is effectively prevented by the rapidly expanding orbifold. We demonstrate that such a transition can be realized for solutions where one boundary potential is negative. For this case, we present two concrete inflationary models which exhibit the transition explicitly.

hep-th↗