arXiv subjects

Carlos Bercini

Publications and source records attributed to Carlos Bercini.

12 recordsLinked to original sources

arXiv2026

Structure Constants from Q-Systems and Separation of Variables

We introduce a novel method to compute structure constants from Q-functions in the scalar sector of planar N=4 super Yang-Mills (SYM) and related theories. The method derives from operatorial as well as functional separation of variables, and the structure constants are expressed as determinants of matrices whose entries are integrals over products of Q-functions. In this framework, each operator is twisted by an external angle, mirroring the cusped Maldacena-Wilson loop. The structure constants of local single-trace operators in N=4 SYM are recovered in the untwisting limit, where we obtain a one-to-one correspondence between our key building blocks and those of the Hexagon formalism. Retaining appropriate twists, our structure constants also perfectly match those of the orbifold points of N=4 SYM. Our results thus far are valid at leading order in the weak-coupling expansion, but their formulation in terms of Q-functions provides a natural starting point for including loop corrections. Many of the methods we develop in this work apply more generally to the computation of correlation functions in integrable models.

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arXiv2025

Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons

We consider higher-point generalizations of the "octagon" large-charge four-point function in planar N=4 super Yang-Mills theory. These n-point polygon correlators are defined as ten-dimensional null limits of generating functions of n-point correlators of protected scalar operators with arbitrary R-charge, and are conjecturally dual to massive scattering amplitudes of W-bosons on the Coulomb branch of the theory. We present a twistor-based direct computation of the polygon loop integrands, and determine the two-loop integrands for any number of external operators. The result is expressed as a linear combination of conformal integrals, with coefficients that are rational functions of the spacetime distances and operator polarizations. We obtain an exact match with a one-loop integrability computation, and study the near-massless limit of the pentagon function.

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arXiv2025

Higher-Point Correlators in N=4 SYM: Generating Functions

We construct generating functions of five- and six-point correlators up to two loops at weak 't Hooft coupling in planar N=4 SYM. These generating functions unify the correlators of the lightest scalar operator in the stress-tensor multiplet with those of all higher R-charge single-trace half-BPS scalar operators, thereby extending previous results for four-point loop integrands. At the integrated level, they are represented as sums of conformal integrals with coefficients exhibiting ten-dimensional poles that combine spacetime and R-charge distances. Our results show that higher-order poles are captured by products of lower-point generating functions. We also extract new OPE data on spinning structure constants, and compare these to integrability-based computations, finding good agreement.

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arXiv2025

Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory

We construct orthogonality relations in the Separation of Variables framework for the sl(2) sector of planar N=4 supersymmetric Yang-Mills theory. Specifically, we find simple universal measures that make Q-functions of operators with different spins vanish at all orders in perturbation theory, prior to wrapping corrections. To analyze this rank-one sector, we relax some of the assumptions thus far considered in the Separation of Variables framework. Our findings may serve as guidelines for extending this formalism to other sectors of the theory as well as other integrable models

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arXiv2024

Wilson Loops with Lagrangians: Large Spin OPE and Cusp Anomalous Dimension Dictionary

In the context of planar conformal gauge theory, we study five-point correlation functions between the interaction Lagrangian and four of the lightest single-trace, gauge-invariant scalar primaries. After performing two light-cone OPEs, we express this correlator in terms of the three-point functions between two leading-twist spinning operators and the Lagrangian. For finite values of spin, we compute these structure constants in perturbation theory up to two loops in N=4 super Yang-Mills theory. Large values of spin are captured by null polygon kinematics, where we use dualities with null polygon Wilson loops as well as factorization properties to bootstrap the universal behavior of the structure constants at all loops. We find explicit maps that relate the Lagrangian structure constants with the leading-twist anomalous dimension. From the large-spin map, we recover the cusp anomalous dimension at strong and weak coupling, including genus-one terms.

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arXiv2024

Two loop five point integrals: light, heavy and large spin correlators

We evaluated all two loop conformal integrals appearing in five point correlation functions of protected operators of $\mathcal{N} = 4$ Super Yang-Mills in several kinematical regimes. Starting from the correlation function of the lightest operators of the theory, we were able to extract structure constants of up to two spinning operators for small and large values of polarizations and spin. We conjectured an universal all loop behaviour for the large spin small polarization structure constants and comment on the subtleties of analytically continuing it from finite to large spin. We also consider correlation functions of heavier operators that get factorized in the more fundamental object called decagon. We fixed this object at two loops in general kinematics and studied its physical properties under OPE and null limits.

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arXiv2022

Structure Constants in $\mathcal{N} = 4$ SYM and Separation of Variables

We propose a new framework for computing three-point functions in planar $\mathcal{N}=4$ super Yang-Mills where these correlators take the form of multiple integrals of Separation of Variables type. We test this formalism at weak coupling at leading and next-to-leading orders in a non-compact SL(2) sector of the theory and all the way to next-to-next-to-leading orders for a compact SU(2) sector. We find evidence that wrapping effects can also be incorporated.

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arXiv2022

Spinning Hexagons

We reduce the computation of three point function of three spinning operators with arbitrary polarizations to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the hexagon partition function. We explore its analytic structure and use it to generate perturbative data for spinning three point functions. For certain polarizations and any coupling, we express the full asymptotic three point function in determinant form. With the integrability approach established we open the ground to study the large spin limit where dualities with null Wilson loops and integrable pentagons must appear.

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arXiv2021

The Wilson Loop -- Large Spin OPE Dictionary

We work out the map between null polygonal hexagonal Wilson loops and spinning three point functions in large $N$ conformal gauge theories by mapping the variables describing the two different physical quantities and by working out the precise normalization factors entering this duality. By fixing all the kinematics we open the ground for a precise study of the dynamics underlying these dualities -- most notably through integrability in the case of planar maximally supersymmetric Yang-Mills theory.

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arXiv2020

Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin

We initiate an exploration of the conformal bootstrap for $n>4$ point correlation functions. Here we bootstrap correlation functions of the lightest scalar gauge invariant operators in planar non-abelian conformal gauge theories as their locations approach the cusps of a null polygon. For that we consider consistency of the OPE in the so-called snowflake channel with respect to cyclicity transformations which leave the null configuration invariant. For general non-abelian gauge theories this allows us to strongly constrain the OPE structure constants of up to three large spin $J_j$ operators (and large polarization quantum number $l_{j}$) to all loop orders. In $ \mathcal{N}=4$ we fix them completely through the duality to null polygonal Wilson loops and the recent origin limit of the hexagon explored by Basso, Dixon and Papathanasiou.

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arXiv2019

SUSY S-matrix Bootstrap and Friends

We consider the 2D S-matrix bootstrap in the presence of supersymmetry, $\mathbb{Z}_2$ and $\mathbb{Z}_4$ symmetry. At the boundary of the allowed S-matrix space we encounter well known integrable models such as the supersymmetric sine-Gordon and restricted sine-Gordon models, novel elliptic deformations thereof, as well as a two parameter family of $\mathbb{Z}_4$ elliptic S-matrices previously proposed by Zamolodchikov. We highlight an intricate web of relations between these various S-matrices.

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arXiv2018

Supersymmetric integrable theories from no particle production

We consider a theory of scalar superfields in two dimensions with arbitrary superpotential. By imposing no particle production in tree level scattering, we constrain the form of the admissible interactions, recovering a supersymmetric extension of the sinh-Gordon model.

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