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The Correlahedron (2017)
Journal Article
Eden, B., Heslop, P., & Mason, L. (2017). The Correlahedron. Journal of High Energy Physics, 2017(9), Article 156. https://doi.org/10.1007/jhep09%282017%29156

We introduce a new geometric object, the correlahedron, which we conjecture to be equivalent to stress-energy correlators in planar N=4N=4 super Yang-Mills. Re-expressing the Grassmann dependence of correlation functions of n chiral stress-energy mul... Read More about The Correlahedron.

Amplitudes and correlators to ten loops using simple, graphical bootstraps (2016)
Journal Article
Bourjaily, J. L., Heslop, P. V., & Tran, V. (2016). Amplitudes and correlators to ten loops using simple, graphical bootstraps. Journal of High Energy Physics, 2016(11), Article 125. https://doi.org/10.1007/jhep11%282016%29125

We introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful... Read More about Amplitudes and correlators to ten loops using simple, graphical bootstraps.

All three-loop four-point correlators of half-BPS operators in planar NN = 4 SYM (2016)
Journal Article
Chicherin, D., Drummond, J., Heslop, P., & Sokatchev, E. (2016). All three-loop four-point correlators of half-BPS operators in planar NN = 4 SYM. Journal of High Energy Physics, 2016(08), Article 053. https://doi.org/10.1007/jhep08%282016%29053

We obtain the planar correlation function of four half-BPS operators of arbitrary weights, up to three loops. Our method exploits only elementary properties of the integrand of the planar correlator, such as its symmetries and singularity structure.... Read More about All three-loop four-point correlators of half-BPS operators in planar NN = 4 SYM.

On-shell diagrams for N = 8 supergravity amplitudes (2016)
Journal Article
Heslop, P., & Lipstein, A. E. (2016). On-shell diagrams for N = 8 supergravity amplitudes. Journal of High Energy Physics, 2016(06), Article 069. https://doi.org/10.1007/jhep06%282016%29069

We define recursion relations for N = 8 supergravity amplitudes using a generalization of the on-shell diagrams developed for planar N = 4 super-Yang-Mills. Although the recursion relations generically give rise to non-planar on-shell diagrams, we sh... Read More about On-shell diagrams for N = 8 supergravity amplitudes.

Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N=4 Supersymmetric Yang-Mills Theory (2016)
Journal Article
Bourjaily, J. L., Heslop, P., & Tran, V. (2016). Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N=4 Supersymmetric Yang-Mills Theory. Physical Review Letters, 116(19), Article 191602. https://doi.org/10.1103/physrevlett.116.191602

We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, confo... Read More about Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N=4 Supersymmetric Yang-Mills Theory.

Bootstrapping correlation functions in N = 4 SYM (2016)
Journal Article
Chicherin, D., Doobary, R., Eden, B., Heslop, P., Korchemsky, G. P., & Sokatchev, E. (2016). Bootstrapping correlation functions in N = 4 SYM. Journal of High Energy Physics, 2016(3), Article 031. https://doi.org/10.1007/jhep03%282016%29031

We describe a new approach to computing the chiral part of correlation functions of stress-tensor supermultiplets in N=4N=4 SYM that relies on symmetries, analytic properties and the structure of the OPE only. We demonstrate that the correlation func... Read More about Bootstrapping correlation functions in N = 4 SYM.

Superconformal partial waves in Grassmannian field theories (2015)
Journal Article
Doobary, R., & Heslop, P. (2015). Superconformal partial waves in Grassmannian field theories. Journal of High Energy Physics, 2015(12), Article 159. https://doi.org/10.1007/jhep12%282015%29159

We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr(m|n, 2m|2n) for all m, n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4N=4 SYM (... Read More about Superconformal partial waves in Grassmannian field theories.

Yangian Symmetry of Scattering Amplitudes and the Dilatation Operator in N=4 Supersymmetric Yang-Mills Theory (2015)
Journal Article
Brandhuber, A., Heslop, P., Travaglini, G., & Young, D. (2015). Yangian Symmetry of Scattering Amplitudes and the Dilatation Operator in N=4 Supersymmetric Yang-Mills Theory. Physical Review Letters, 115(14), Article 141602. https://doi.org/10.1103/physrevlett.115.141602

It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S matrix of N=4 super Yang-Mills theory. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up... Read More about Yangian Symmetry of Scattering Amplitudes and the Dilatation Operator in N=4 Supersymmetric Yang-Mills Theory.

Correlation functions of the chiral stress-tensor multiplet in N=4 SYM (2015)
Journal Article
Chicherin, D., Doobary, R., Eden, B., Heslop, P., Korchemsky, G., Mason, L., & Sokatchev, E. (2015). Correlation functions of the chiral stress-tensor multiplet in N=4 SYM. Journal of High Energy Physics, 2015, Article 198. https://doi.org/10.1007/jhep06%282015%29198

We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum o... Read More about Correlation functions of the chiral stress-tensor multiplet in N=4 SYM.

Local integrands for the five-point amplitude in planar N=4 SYM up to five loops (2015)
Journal Article
Ambrosio, R. G., Eden, B., Goddard, T., Heslop, P., & Taylor, C. (2015). Local integrands for the five-point amplitude in planar N=4 SYM up to five loops. Journal of High Energy Physics, 2015(1), Article 116. https://doi.org/10.1007/jhep01%282015%29116

Integrands for colour ordered scattering amplitudes in planar N=4 SYM are dual to those of correlation functions of the energy-momentum multiplet of the theory. The construction can relate amplitudes with different numbers of legs. By graph theory me... Read More about Local integrands for the five-point amplitude in planar N=4 SYM up to five loops.

Leading singularities and off-shell conformal integrals (2013)
Journal Article
Drummond, J., Duhr, C., Eden, B., Heslop, P., Pennington, J., & Smirnov, V. A. (2013). Leading singularities and off-shell conformal integrals. Journal of High Energy Physics, 2013(8), Article 133. https://doi.org/10.1007/jhep08%282013%29133

The three-loop four-point function of stress-tensor multiplets in N = 4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integr... Read More about Leading singularities and off-shell conformal integrals.

The super-correlator/super-amplitude duality: Part II. (2013)
Journal Article
Eden, B., Heslop, P., Korchemsky, G. P., & Sokatchev, E. (2013). The super-correlator/super-amplitude duality: Part II. Nuclear Physics B, 869(3), 378-416. https://doi.org/10.1016/j.nuclphysb.2012.12.014

We continue the study of the duality between super-correlators and scattering super-amplitudes in planar N=4 SYM. We provide a number of further examples supporting the conjectured duality relation between these two seemingly different objects. We co... Read More about The super-correlator/super-amplitude duality: Part II..

The super-correlator/super-amplitude duality: Part I. (2013)
Journal Article
Eden, B., Heslop, P., Korchemsky, G. P., & Sokatchev, E. (2013). The super-correlator/super-amplitude duality: Part I. Nuclear Physics B, 869(3), 329-377. https://doi.org/10.1016/j.nuclphysb.2012.12.015

We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider the natural generali... Read More about The super-correlator/super-amplitude duality: Part I..

Perturbative correlation functions of null Wilson loops and local operators (2013)
Journal Article
Alday, L., Heslop, P., & Sikorowski, J. (2013). Perturbative correlation functions of null Wilson loops and local operators. Journal of High Energy Physics, 2013(3), Article 074. https://doi.org/10.1007/jhep03%282013%29074

We consider the correlation function of a null Wilson loop with four edges and a local operator in planar MSYM. By applying the insertion procedure, developed for correlation functions of local operators, we give an integral representation for the re... Read More about Perturbative correlation functions of null Wilson loops and local operators.

Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM (2012)
Journal Article
Eden, B., Heslop, P., Korchemsky, G. P., & Sokatchev, E. (2012). Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM. Nuclear Physics B, 862(2), 450-503. https://doi.org/10.1016/j.nuclphysb.2012.04.013

We present a construction of the integrand of the correlation function of four stress-tensor multiplets in N=4 SYM at weak coupling. It does not rely on Feynman diagrams and makes use of the recently discovered symmetry of the integrand under permuta... Read More about Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM.

Five-loop Konishi in N=4 SYM (2012)
Journal Article
Eden, B., Heslop, P., Korchemsky, G. P., Smirnov, V. A., & Sokatchev, E. (2012). Five-loop Konishi in N=4 SYM. Nuclear Physics B, 862(1), 123-166. https://doi.org/10.1016/j.nuclphysb.2012.04.015

We present a new method for computing the Konishi anomalous dimension in N=4 SYM at weak coupling. It does not rely on the conventional Feynman diagram technique and is not restricted to the planar limit. It is based on the OPE analysis of the four-p... Read More about Five-loop Konishi in N=4 SYM.