723 research outputs found

### A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are
believed to belong to a special class of generalised polylogarithm functions
called heptagon functions. These are functions with physical branch cuts whose
symbols may be written in terms of the 42 cluster A-coordinates on Gr(4,7).
Motivated by the success of the hexagon bootstrap programme for constructing
six-particle amplitudes we initiate the systematic study of the symbols of
heptagon functions. We find that there is exactly one such symbol of weight six
which satisfies the MHV last-entry condition and is finite in the $7 \parallel
6$ collinear limit. This unique symbol is both dihedral and parity-symmetric,
and remarkably its collinear limit is exactly the symbol of the three-loop
six-particle MHV amplitude, although none of these properties were assumed a
priori. It must therefore be the symbol of the three-loop seven-particle MHV
amplitude. The simplicity of its construction suggests that the n-gon bootstrap
may be surprisingly powerful for n>6.Comment: 30 pages, 3 ancillary files, v3: minor corrections, including a typo
in (33

### Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory

We describe the hexagon function bootstrap for solving for six-gluon
scattering amplitudes in the large $N_c$ limit of ${\cal N}=4$ super-Yang-Mills
theory. In this method, an ansatz for the finite part of these amplitudes is
constrained at the level of amplitudes, not integrands, using boundary
information. In the near-collinear limit, the dual picture of the amplitudes as
Wilson loops leads to an operator product expansion which has been solved using
integrability by Basso, Sever and Vieira. Factorization of the amplitudes in
the multi-Regge limit provides additional boundary data. This bootstrap has
been applied successfully through four loops for the maximally helicity
violating (MHV) configuration of gluon helicities, and through three loops for
the non-MHV case.Comment: 15 pages, 3 figures, 2 tables; contribution to the proceedings of
Loops and Legs in Quantum Field Theory, 27 April - 2 May 2014, Weimar,
Germany; v2, reference adde

### Kappa-symmetric deformations of M5-brane dynamics

We calculate the first supersymmetric and kappa-symmetric derivative
deformation of the M5-brane worldvolume theory in a flat eleven-dimensional
background. By applying cohomological techniques we obtain a deformation of the
standard constraint of the superembedding formalism. The first possible
deformation of the constraint and hence the equations of motion arises at cubic
order in fields and fourth order in a fundamental length scale $l$. The
deformation is unique up to this order. In particular this rules out any
induced Einstein-Hilbert terms on the worldvolume. We explicitly calculate
corrections to the equations of motion for the tensor gauge supermultiplet.Comment: 17 pages. Additional comments in section

### 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

### Magic identities for conformal four-point integrals

We propose an iterative procedure for constructing classes of off-shell
four-point conformal integrals which are identical. The proof of the identity
is based on the conformal properties of a subintegral common for the whole
class. The simplest example are the so-called `triple scalar box' and `tennis
court' integrals. In this case we also give an independent proof using the
method of Mellin--Barnes representation which can be applied in a similar way
for general off-shell Feynman integrals.Comment: 13 pages, 12 figures. New proof included with neater discussion of
contact terms. Typo correcte

### The four-loop remainder function and multi-Regge behavior at NNLLA in planar $\mathcal{N}$ = 4 super-Yang-Mills theory

We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar N = 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N3LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory

### New differential equations for on-shell loop integrals

We present a novel type of differential equations for on-shell loop
integrals. The equations are second-order and importantly, they reduce the loop
level by one, so that they can be solved iteratively in the loop order. We
present several infinite series of integrals satisfying such iterative
differential equations. The differential operators we use are best written
using momentum twistor space. The use of the latter was advocated in recent
papers discussing loop integrals in N=4 super Yang-Mills. One of our
motivations is to provide a tool for deriving analytical results for scattering
amplitudes in this theory. We show that the integrals needed for planar MHV
amplitudes up to two loops can be thought of as deriving from a single master
topology. The master integral satisfies our differential equations, and so do
most of the reduced integrals. A consequence of the differential equations is
that the integrals we discuss are not arbitrarily complicated transcendental
functions. For two specific two-loop integrals we give the full analytic
solution. The simplicity of the integrals appearing in the scattering
amplitudes in planar N=4 super Yang-Mills is strongly suggestive of a relation
to the conjectured underlying integrability of the theory. We expect these
differential equations to be relevant for all planar MHV and non-MHV
amplitudes. We also discuss possible extensions of our method to more general
classes of integrals.Comment: 39 pages, 8 figures; v2: typos corrected, definition of harmonic
polylogarithms adde

### Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

Tree-level scattering amplitudes in N=4 super Yang-Mills theory have recently
been shown to transform covariantly with respect to a 'dual' superconformal
symmetry algebra, thus extending the conventional superconformal symmetry
algebra psu(2,2|4) of the theory. In this paper we derive the action of the
dual superconformal generators in on-shell superspace and extend the dual
generators suitably to leave scattering amplitudes invariant. We then study the
algebra of standard and dual symmetry generators and show that the inclusion of
the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a
Yangian. The non-local Yangian generators acting on amplitudes turn out to be
cyclically invariant due to special properties of psu(2,2|4). The
representation of the Yangian generators takes the same form as in the case of
local operators, suggesting that the Yangian symmetry is an intrinsic property
of planar N=4 super Yang-Mills, at least at tree level.Comment: 23 pages, no figures; v2: typos corrected, references added; v3:
minor changes, references adde

### Behavioural analysis and regulatory impact assessment

Published online: 22 March 2024Regulatory impact assessment (RIA) is an appraisal tool to bring evidence to bear on regulatory decisions. A key property of RIA is that is corrects errors in reasoning by pushing regulators towards deliberative thinking to override intuitive judgments. However, the steps for regulatory analysis suggested by international organisations and governmental handbooks do not handle two sources of bias and barriers that are well documented in the literature on behavioural insights. First, bias enters the process via knowledge production during the analytical process of assessment. Second, bias affects knowledge utilisation when regulators âreadâ or utilise the results of RIA. We explore these two pathways by focusing on drivers of behaviour rather than lists of biases. The conclusions reflect on the limitations of current practice and its possible improvement, making suggestions for an RIA architecture that is fully informed by behavioural analysis.This article was published Open Access with the support from the EUI Library through the CRUI - CUP Transformative Agreement (2023-2025

### The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes

We review the bootstrap method for constructing six- and seven-particle
amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory, by exploiting
their analytic structure. We focus on two recently discovered properties which
greatly simplify this construction at symbol and function level, respectively:
the extended Steinmann relations, or equivalently cluster adjacency, and the
coaction principle. We then demonstrate their power in determining the
six-particle amplitude through six and seven loops in the NMHV and MHV sectors
respectively, as well as the symbol of the NMHV seven-particle amplitude to
four loops.Comment: 36 pages, 4 figures, 5 tables, 1 ancillary file. Contribution to the
proceedings of the Corfu Summer Institute 2019 "School and Workshops on
Elementary Particle Physics and Gravity" (CORFU2019), 31 August - 25
September 2019, Corfu, Greec

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