arXiv subjects

Simon Caron-Huot

Publications and source records attributed to Simon Caron-Huot.

At least 55 records · Page 3Linked to original sources

arXiv2020

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.

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arXiv2019

The High-Energy Limit of 2-to-2 Partonic Scattering Amplitudes

Recently, there has been significant progress in computing scattering amplitudes in the high-energy limit using rapidity evolution equations. We describe the state-of-the-art and demonstrate the interplay between exponentiation of high-energy logarithms and that of infrared singularities. The focus in this talk is the imaginary part of 2 to 2 partonic amplitudes, which can be determined by solving the BFKL equation. We demonstrate that the wavefunction is infrared finite, and that its evolution closes in the soft approximation. Within this approximation we derive a closed-form solution for the amplitude in dimensional regularization, which fixes the soft anomalous dimension to all orders at NLL accuracy. We then turn to finite contributions of the amplitude and show that the remaining hard contributions can be determined algorithmically, by iteratively solving the BFKL equation in exactly two dimensions within the class of single-valued harmonic polylogarithms. To conclude we present numerical results and analyse large-order behaviour of the amplitude.

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arXiv2019

The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N} = 4$ SYM Amplitudes

We describe the minimal space of polylogarithmic functions that is required to express the six-particle amplitude in planar ${\cal N}=4$ super-Yang-Mills theory through six and seven loops, in the NMHV and MHV sectors respectively. This space respects a set of extended Steinmann relations that restrict the iterated discontinuity structure of the amplitude, as well as a cosmic Galois coaction principle that constrains the functions and the transcendental numbers that can appear in the amplitude at special kinematic points. To put the amplitude into this space, we must divide it by the BDS-like ansatz and by an additional zeta-valued constant $ρ$. For this normalization, we conjecture that the extended Steinmann relations and the coaction principle hold to all orders in the coupling. We describe an iterative algorithm for constructing the space of hexagon functions that respects both constraints. We highlight further simplifications that begin to occur in this space of functions at weight eight, and distill the implications of imposing the coaction principle to all orders. Finally, we explore the restricted spaces of transcendental functions and constants that appear in special kinematic configurations, which include polylogarithms involving square, cube, fourth and sixth roots of unity.

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arXiv2019

Six-Gluon Amplitudes in Planar ${\cal N}=4$ Super-Yang-Mills Theory at Six and Seven Loops

We compute the six-particle maximally-helicity-violating (MHV) and next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills theory through seven loops and six loops, respectively, as an application of the extended Steinmann relations and using the cosmic Galois coaction principle. Starting from a minimal space of functions constructed using these principles, we identify the amplitude by matching its symmetries and predicted behavior in various kinematic limits. Through five loops, the MHV and NMHV amplitudes are uniquely determined using only the multi-Regge and leading collinear limits. Beyond five loops, the MHV amplitude requires additional data from the kinematic expansion around the collinear limit, which we obtain from the Pentagon Operator Product Expansion, and in particular from its single-gluon bound state contribution. We study the MHV amplitude in the self-crossing limit, where its singular terms agree with previous predictions. Analyzing and plotting the amplitudes along various kinematical lines, we continue to find remarkable stability between loop orders.

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arXiv2018

Integrability of Black Hole Orbits in Maximal Supergravity

We study the dynamics of a pair of extremal (half-BPS) black holes in $\mathcal{N}=8$ supergravity, as a potentially solvable model of gravitational dynamics. As a diagnosis of hidden symmetries, we ask whether the perihelion of the orbits precesses over time. We consider black hole charge vectors with arbitrary misalignment. First, we use scattering amplitude methods to compute the leading post-Newtonian correction for general mass ratios. This computation is greatly simplified by introducing a suitable on-shell superspace. Second, we study the probe limit to all orders in velocity and Newton's constant through a ten-dimensional brane setup. In all cases we find no precession. We relate this to the absence of scalar triangle integrals.

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arXiv2018

All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry

We study correlators of four protected (half-BPS) operators in strongly coupled supersymmetric Yang-Mills theory. These are dual to tree-level supergravity amplitudes on AdS${}_5\times$S${}_5$ for various spherical harmonics on the five-sphere. We use conformal field theory methods, in particular a recently obtained Lorentzian inversion formula, to analytically bootstrap these correlators. The extracted $1/N^2$ double-trace anomalous dimensions confirm a simple pattern recently conjectured by Aprile, Drummond, Heslop and Paul. We explain this pattern by an unexpected ten-dimensional conformal symmetry which appears to be enjoyed by tree-level supergravity (or a suitable subsector of it). The symmetry combines all spherical harmonics into a single ten-dimensional object, and yields compact expressions for the leading logarithmic part of any half-BPS correlator at each loop order.

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arXiv2018

The Double Pentaladder Integral to All Orders

We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N=4 super-Yang-Mills theory. We provide exact, finite-coupling formulas for the basic double pentaladder integrals as a single Mellin integral over hypergeometric functions. For particular choices of the dual conformal cross ratios, we can evaluate the integral at weak coupling to high loop orders in terms of multiple polylogarithms. We argue that the integrals are exponentially suppressed at strong coupling. We describe the space of functions that contains all such double pentaladder integrals and their derivatives, or coproducts. This space, a prototype for the space of Steinmann hexagon functions, has a simple algebraic structure, which we elucidate by considering a particular discontinuity of the functions that localizes the Mellin integral and collapses the relevant symbol alphabet. This function space is endowed with a coaction, both perturbatively and at finite coupling, which mixes the independent solutions of the hypergeometric differential equation and constructively realizes a coaction principle of the type believed to hold in the full Steinmann hexagon function space.

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arXiv2018

Resummation of non-global logarithms and the BFKL equation

We consider a `color density matrix' in gauge theory. We argue that it systematically resums large logarithms originating from wide-angle soft radiation, sometimes referred to as non-global logarithms, to all logarithmic orders. We calculate its anomalous dimension at leading- and next-to-leading order. Combined with a conformal transformation known to relate this problem to shockwave scattering in the Regge limit, this is used to rederive the next-to-leading order Balitsky-Fadin-Kuraev-Lipatov equation (including its nonlinear generalization, the so-called Balitsky-JIMWLK equation), finding perfect agreement with the literature. Exponentiation of divergences to all logarithmic orders is demonstrated. The possibility of obtaining the evolution equation (and BFKL) to three-loop is discussed.

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arXiv2018

High-energy evolution to three loops

The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to this equation in planar $\mathcal{N}=4$ super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the three-loop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in cross-section calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.

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arXiv2018

Analyticity in Spin in Conformal Theories

Conformal theory correlators are characterized by the spectrum and three- point functions of local operators. We present a formula which extracts this data as an analytic function of spin. In analogy with a classic formula due to Froissart and Gribov, it is sensitive only to an "imaginary part" which appears after analytic continuation to Lorentzian signature, and it converges thanks to recent bounds on the high-energy Regge limit. At large spin, substituting in cross-channel data, the formula yields 1/J expansions with controlled errors. In large-N theories, the imaginary part is saturated by single-trace operators. For a sparse spectrum, it manifests the suppression of bulk higher-derivative interactions that constitutes the signature of a local gravity dual in Anti-de-Sitter space.

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arXiv2018

Subleading Regge limit from a soft anomalous dimension

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.

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arXiv2017

Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders

Scattering amplitudes of partons in QCD contain infrared divergences which can be resummed to all orders in terms of an anomalous dimension. Independently, in the limit of high-energy forward scattering, large logarithms of the energy can be resummed using Balitsky-Fadin-Kuraev-Lipatov theory. We use the latter to analyze the infrared-singular part of amplitudes to all orders in perturbation theory and to next-to-leading-logarithm accuracy in the high-energy limit, resumming the two-Reggeon contribution. Remarkably, we find a closed form for the infrared-singular part, predicting the Regge limit of the soft anomalous dimension to any loop order.

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arXiv2017

Gravitational S-matrix from CFT dispersion relations

We analyse the double-discontinuities of the four-point correlator of the stress-tensor multiplet in N=4 SYM at large t' Hooft coupling and at order $1/N^4$, as a way to access one-loop effects in the dual supergravity theory. From these singularities we extract CFT-data by using two inversion procedures: one based on a recently proposed Froissart-Gribov inversion integral, and the other based on large spin perturbation theory. Both procedures lead to the same results and are shown to be equivalent more generally. Our computation parallels the standard S-matrix reconstruction via dispersion relations. In a suitable limit, the result of the conformal field theory calculation is compared with the one-loop graviton scattering amplitude in ten-dimensional IIB supergravity in flat space, finding perfect agreement.

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arXiv2017

Renormalization group coefficients and the S-matrix

We show how to use on-shell unitarity methods to calculate renormalization group coefficients such as beta functions and anomalous dimensions. The central objects are the form factors of composite operators. Their discontinuities can be calculated via phase-space integrals and are related to corresponding anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is given by minus the phase of the S-matrix divided by pi. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond.

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arXiv2017

Two-parton scattering in the high-energy limit

Considering $2\to 2$ gauge-theory scattering with general colour in the high-energy limit, we compute the Regge-cut contribution to three loops through next-to-next-to-leading high-energy logarithms (NNLL) in the signature-odd sector. Our formalism is based on using the non-linear Balitsky-JIMWLK rapidity evolution equation to derive an effective Hamiltonian acting on states with a fixed number of Reggeized gluons. A new effect occurring first at NNLL is mixing between states with $k$ and $k+2$ Reggeized gluons due non-diagonal terms in this Hamiltonian. Our results are consistent with a recent determination of the infrared structure of scattering amplitudes at three loops, as well as a computation of $2\to 2$ gluon scattering in ${\cal N}=4$ super Yang-Mills theory. Combining the latter with our Regge-cut calculation we extract the three-loop Regge trajectory in this theory. Our results open the way to predict high-energy logarithms through NNLL at higher-loop orders.

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arXiv2016

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations

The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function bootstrap in planar maximally supersymmetric Yang-Mills theory. Armed with this simplification, along with the constraints of dual conformal symmetry and Regge exponentiation, we obtain the complete five-loop six-particle amplitude.

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arXiv2016

Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude

We consider weakly-coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime $s,t \gg 1$, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, $j(t)$, is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higher-spin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.

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arXiv2015

New Representations of the Perturbative S-Matrix

We propose a new framework to represent the perturbative S-matrix which is well-defined for all quantum field theories of massless particles, constructed from tree-level amplitudes and integrable term-by-term. This representation is derived from the Feynman expansion through a series of partial fraction identities, discarding terms that vanish upon integration. Loop integrands are expressed in terms of "Q-cuts" that involve both off-shell and on-shell loop-momenta, defined with a precise contour prescription that can be evaluated by ordinary methods. This framework implies recent results found in the scattering equation formalism at one-loop, and it has a natural extension to all orders---even non-planar theories without well-defined forward limits or good ultraviolet behavior.

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