arXiv subjects

Emery Sokatchev

Publications and source records attributed to Emery Sokatchev.

At least 19 recordsLinked to original sources

arXiv2025

Energy correlators in four-dimensional gravity

We investigate energy correlators in four-dimensional gravitational theories, which provide a simple class of infrared-finite observables. We compute the one- and two-point energy correlators at one loop in $\mathcal{N}=8$ supergravity and in pure Einstein gravity, with particular emphasis on the contact terms arising from the interplay between virtual corrections and real emissions. We explicitly demonstrate the cancellation of infrared divergences and verify the Ward identities associated with energy-momentum conservation. In the back-to-back limit, we derive an all-order expression for the energy-energy correlator, showing that it is governed by universal soft-graviton dynamics. We further introduce a particularly simple beam-averaged energy-energy correlator and compute it in different gravitational theories, including tree-level string theory. The resulting correlators exhibit analyticity and polynomial boundedness, allowing for the formulation of dispersion relations, which we explore. Finally, we discuss additional singularities of the gravitational energy correlators, absent in QCD, that originate from the long-range nature of the gravitational interactions.

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arXiv2024

The Collinear Limit of the Four-Point Energy Correlator in $\mathcal{N} = 4$ Super Yang-Mills Theory

We present a compact formula, expressed in terms of classical polylogarithms up to weight three, for the leading order four-point energy correlator in maximally supersymmetric Yang-Mills theory, in the limit where the four detectors are collinear. This formula is derived by combining a simplified, manifestly dual conformal invariant form of the 1 -> 4 splitting function obtained from the square of the tree-level five-particle form factor of stress-tensor multiplet operators, with a novel integration-by-parts algorithm operating directly on Feynman parameter integrals. Our results provide valuable data for exploring the structure of physical observables in perturbation theory, and for calculations of jet substructure observables in quantum chromodynamics.

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arXiv2021

Generalizing event shapes: In search of lost collider time

We introduce a new class of collider-type observables in conformal field theories which we call generalized event shapes. They are defined as matrix elements of light-ray operators that are sensitive to the longitudinal, or time-dependent, structure of the state produced in the collision. Generalized event shapes can be studied using both correlation functions and scattering amplitudes. They are infrared finite and smoothly transit over to the familiar event shapes. We compute them in planar ${\cal N}=4$ super-Yang-Mills theory at weak and strong coupling, and study their physical properties. We show that at strong coupling both the stringy and quantum-gravitational corrections to the energy-energy correlation exhibit longitudinal broadening that manifests itself through the presence of long-time tails in the energy flux measured by the detectors.

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arXiv2020

Conformal anomaly of pseudo-scalar operators

We study the conformal properties of pseudo-scalar (parity-odd) operators in four-dimensional field theory. Such operators include the topological term in a gauge theory and the Yukawa coupling. We show that a single operator of this type cannot be a conformal primary on its own. This is only possible for certain mixtures of pseudo-scalar operators like the chiral Lagrangian of ${\cal N}=4$ super-Yang-Mills theory. We examine the detailed mechanism of conformal symmetry breakdown and derive an anomalous conformal Ward identity. We explore a possible link between this conformal anomaly and the axial anomaly.

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arXiv2019

Energy-energy correlations at next-to-next-to-leading order

We develop further an approach to computing energy-energy correlations (EEC) directly from finite correlation functions. In this way, one completely avoids infrared divergences. In maximally supersymmetric Yang-Mills theory ($\mathcal{N}=4$ sYM), we derive a new, extremely simple formula relating the EEC to a triple discontinuity of a four-point correlation function. We use this formula to compute the EEC in $\mathcal{N}=4$ sYM at next-to-next-to-leading order in perturbation theory. Our result is given by a two-fold integral representation that is straightforwardly evaluated numerically. We find that some of the integration kernels are equivalent to those appearing in sunrise Feynman integrals, which evaluate to elliptic functions. Finally, we use the new formula to provide the expansion of the EEC in the back-to-back and collinear limits.

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arXiv2018

Amplitudes from anomalous superconformal symmetry

We initiate a systematic study of the consequences of (super)conformal symmetry of massless scattering amplitudes. The classical symmetry is potentially broken at the quantum level by infrared and ultraviolet effects. We study its manifestations on the finite hard part of the scattering process. The conformal Ward identities in momentum space are second-order differential equations, difficult to analyze. We prefer to study superconformal symmetry whose generators are first-order in the momenta. Working in a massless N=1 supersymmetric Wess-Zumino model, we derive on-shell superconformal Ward identities. They contain an anomaly due to collinear regions of loop momenta. It is given by an integral with one loop less than the original graph, with an extra integral over a collinear splitting parameter. We discuss the relation to the holomorphic anomaly that was previously studied in tree-level amplitudes and at the level of unitarity cuts. We derive and solve Ward identities for various scattering processes in the model. We classify the on-shell superamplitudes according to their Grassmann degree, in close analogy with the helicity classification of gluon amplitudes. We focus on MHV-like and NMHV-like amplitudes with up to six external particles, at one and two loops. Interestingly, the superconformal generator acting on the bosonic part of the amplitudes is Witten's twistor collinearity operator. We find that the first-order differential equations, together with physically motivated boundary conditions, uniquely fix the answer. All the cases considered give rise to uniform weight functions. Our most interesting example is a five-point non-planar hexa-box integral with an off-shell leg. It gives first indications on the function space needed for Higgs plus two jet production at next-to-next-to leading order.

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arXiv2018

Implications of nonplanar dual conformal symmetry

Recently, Bern et al observed that a certain class of next-to-planar Feynman integrals possess a bonus symmetry that is closely related to dual conformal symmetry. It corresponds to a projection of the latter along a certain lightlike direction. Previous studies were performed at the level of the loop integrand, and a Ward identity for the integral was formulated. We investigate the implications of the symmetry at the level of the integrated quantities. In particular, we focus on the phenomenologically important case of five-particle scattering. The symmetry simplifies the four-variable problem to a three-variable one. In the context of the recently proposed space of pentagon functions, the symmetry is much stronger. We find that it drastically reduces the allowed function space, leading to a well-known space of three-variable functions. Furthermore, we show how to use the symmetry in the presence of infrared divergences, where one obtains an anomalous Ward identity. We verify that the Ward identity is satisfied by the leading and subleading poles of several nontrivial five-particle integrals. Finally, we present examples of integrals that possess both ordinary and dual conformal symmetry.

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arXiv2018

Amplitudes from superconformal Ward identities

We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Due to on-shell collinear singularities, the Ward identities have an anomaly, which is obtained from lower-loop information. We show that in the five-particle case, the solution to the equations is uniquely fixed by the expected analytic behavior. We apply the method to a non-planar two-loop five-particle integral.

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arXiv2017

Conformal anomaly of generalized form factors and finite loop integrals

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an $\ell-$loop integral is a 2nd-order differential equation whose right-hand side is an $(\ell-1)-$loop integral. We show several examples, in particular the four-dimensional scalar double box.

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arXiv2017

N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory

We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.

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arXiv2017

N=4 super-Yang-Mills in LHC superspace. Part II: Non-chiral correlation functions of the stress-tensor multiplet

We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.

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arXiv2016

Wilson Loop Form Factors: A New Duality

We find a new duality for form factors of lightlike Wilson loops in planar $\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analytic continuation from Minkowski to Euclidean space. We illustrate all of these subtleties explicitly in the simplest non-trivial NMHV-like case.

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arXiv2016

Composite operators and form factors in N=4 SYM

We construct the most general composite operators of N = 4 SYM in Lorentz harmonic chiral ($\approx$ twistor) superspace. The operators are built from the SYM supercurvature which is nonpolynomial in the chiral gauge prepotentials. We reconstruct the full nonchiral dependence of the supercurvature. We compute all tree-level MHV form factors via the LSZ redcution procedure with on-shell states made of the same supercurvature.

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arXiv2016

Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory

We explain some details of the construction of composite operators in N=4 SYM that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC) superspace. We give a step-by-step elementary derivation and show that the result coincides with the recent hypothesis put forward in arXiv:1603.04471 within the twistor approach. We provide the appropriate LHC-to-twistors dictionary.

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arXiv2015

All three-loop four-point correlators of half-BPS operators in planar N=4 SYM

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. This allows us to write down a general ansatz for the integrand. The coefficients in the ansatz are fixed by means of a powerful light-cone OPE relation between correlators with different weights. Our result is formulated in terms of a limited number of functions built from known one-, two- and three-loop conformal integrals. These results are useful for checking recent integrability predictions for the OPE structure constants.

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arXiv2015

Bootstrapping correlation functions in N=4 SYM

We describe a new approach to computing the chiral part of correlation functions of stress-tensor supermultiplets in N=4 SYM that relies on symmetries, analytic properties and the structure of the OPE only. We demonstrate that the correlation functions are given by a linear combination of chiral N=4 superconformal invariants accompanied by coefficient functions depending on the space-time coordinates only. We present the explicit construction of these invariants and show that the six-point correlation function is fixed in the Born approximation up to four constant coefficients by its symmetries. In addition, the known asymptotic structure of the correlation function in the light-like limit fixes unambiguously these coefficients up to an overall normalization. We demonstrate that the same approach can be applied to obtain a representation for the six-point NMHV amplitude that is free from any auxiliary gauge fixing parameters, does not involve spurious poles and manifests half of the dual superconformal symmetry.

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arXiv2014

A note on four-point correlators of half-BPS operators in N=4 SYM

We calculate the four-point correlation function of half-BPS operators with weights 2, 3, 3, 4 in N=4 SYM to two-loop order. The OPE of this correlation function provides a nontrivial check of the integrability conjecture for a class of three-point functions formulated in arXiv:1311.6404. Our perturbative calculation exploits the supergraph formalism in N=2 harmonic superspace.

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arXiv2014

From correlation functions to scattering amplitudes

We study the correlators of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the loop corrections by means of Lagrangian insertions. The divergences resulting from the light-cone limit are regularized by changing the dimension of the integration measure over the insertion points. Switching from coordinates to dual momenta, we show that the logarithm of the correlator is identical with twice the logarithm of the matching MHV gluon scattering amplitude. We present a number of examples of this new relation, at one and two loops.

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