arXiv subjects

Gwenaël Ferrando

Publications and source records attributed to Gwenaël Ferrando.

10 recordsLinked to original sources

arXiv2026

Exact Defect Correlation Functions in Chern-Simons Matter Theories

We study defect correlators in three-dimensional, large-$N$, conformal field theories with slightly broken higher-spin symmetry. Focusing on the quasi-fermionic theory, we bootstrap correlation functions of four defect-changing operators, i.e. of two collinear conformal line defects with boundaries, at arbitrary values of the coupling constant. We can compute an infinite number of such correlators and present a detailed analysis for three typical cases. In addition, we obtain some defect OPE coefficients that give us access to the relative conformal dimension between defect-changing operators at order $O(1/N)$. In the course of our analysis, we also derive explicit expressions for some Feynman integrals that might be of independent interest, including an extension of the usual star-triangle relation. Our bootstrap assumptions naturally apply to Chern-Simons matter theories, so our results provide a non-trivial example of explicit, non-perturbative defect four-point functions in a strongly coupled gauge theory.

hep-th↗

arXiv2025

Hypergeometry from $\mathrm{\widehat P}$-Symmetry: Feynman Integrals in One and Two Dimensions

Feynman integrals with generic propagator powers in one and two spacetime dimensions are investigated from various perspectives. In particular, we argue that the class of track integrals at any loop order is fixed by the recently found $\mathrm{\widehat P}$-symmetries of Yangian type. All track integrals up to six external points (and four loops) are bootstrapped explicitly as well as the full family of one-loop integrals at any multiplicity. Moreover, the triangle tracks at generic loop order, which constitute the most generic family of track-type integrals, are bootstrapped in this way. The results are compared to the direct evaluation via a `spectral transform' from the integrability toolbox that turns out to be particularly efficient for position-space tree integrals in lower dimensions. We prove that all $\mathrm{\widehat P}$-symmetries of these integrals can be derived from the framework of Aomoto--Gelfand hypergeometric functions, which applies to integrals in one and two dimensions. Finally, we also demonstrate the method's applicability to conformal integrals by deriving the complete results for all comb-channel conformal partial waves as well as the conformal double-box integral. We explicitly go through all examples of the above integrals in 1D and then provide a straightforward recipe for how to read off their 2D counterparts.

hep-th↗

arXiv2025

Exact Three-Point Functions in $\mathcal{N}=2$ Superconformal Field Theories: Integrability vs. Localization

We propose an integrability approach for planar three-point functions at finite coupling in $\mathcal{N}=2$ superconformal field theories obtained as $\mathbb{Z}_K$ orbifolds of $\mathcal{N}=4$ super Yang-Mills (SYM). Generalizing the hexagon formalism for $\mathcal{N}=4$ SYM, we reproduce the structure constants of Coulomb branch operators, previously obtained by supersymmetric localization, as exact functions of the 't Hooft coupling. Our analysis explains the common physical origin of Fredholm kernels in integrability and localization, and hints at structures after the resummation in the hexagon formalism.

hep-th↗

arXiv2025

Correlators of Line Defect and Local Operator in Conformal Field Theories with a Slightly Broken Higher-Spin Symmetry

We study three-dimensional conformal field theories with a large-$N$ limit. Leveraging the framework of slightly broken higher-spin symmetry, we bootstrap correlation functions between the single-trace, local operators and straight, conformal line defects with boundaries. These correlation functions, which depend on a single conformal cross-ratio, encapsulate all bulk-defect operator product expansion coefficients. Concentrating on the quasi-fermionic theory, we explicitly compute all correlators involving the spin-zero and spin-one conserved currents, along with an infinite family of correlators involving the higher-spin currents. Furthermore, we demonstrate that the dependence of these correlators on the defect's shape is fully determined by our bootstrap constraints.

hep-th↗

arXiv2025

Bethe ansatz inside Calogero-Sutherland models

We study the trigonometric quantum spin-Calogero-Sutherland model, and the Haldane-Shastry spin chain as a special case, using a Bethe-ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability for Heisenberg spin chains into the world of integrable long-range models with spins. From the transfer matrix with a diagonal twist we construct Heisenberg-style symmetries (Bethe algebra) that refine the usual hierarchy of commuting Hamiltonians (quantum determinant) of the spin-Calogero-Sutherland model. We compute the first few of these new conserved charges explicitly, and diagonalise them by Bethe ansatz inside each irreducible Yangian representation. This yields a new eigenbasis for the spin-Calogero-Sutherland model that generalises the Yangian Gelfand-Tsetlin basis of Takemura-Uglov. The Bethe-ansatz analysis involves non-generic values of the inhomogeneities. Our review of the inhomogeneous Heisenberg XXX chain, with special attention to how the Bethe ansatz works in the presence of fusion, may be of independent interest.

math-ph↗

arXiv2025

Checkerboard CFT

The Checkerboard conformal field theory is an interesting representative of a large class of non-unitary, logarithmic Fishnet CFTs (FCFT) in arbitrary dimension which have been intensively studied in the last years. Its planar Feynman graphs have the structure of a regular square lattice with checkerboard colouring. Such graphs are integrable since each coloured cell of the lattice is equal to an R-matrix in the principal series representations of the conformal group. We compute perturbatively and numerically the anomalous dimension of the shortest single-trace operator in two reductions of the Checkerboard CFT: the first one corresponds to the Fishnet limit of the twisted ABJM theory in 3D, whereas the spectrum in the second, 2D reduction contains the energy of the BFKL Pomeron. We derive an analytic expression for the Checkerboard analogues of Basso--Dixon 4-point functions, as well as for the class of Diamond-type 4-point graphs with disc topology. The properties of the latter are studied in terms of OPE for operators with open indices. We prove that the spectrum of the theory receives corrections only at even orders in the loop expansion and we conjecture such a modification of Checkerboard CFT where quantum corrections occur only with a given periodicity in the loop order.

hep-th↗

arXiv2023

A Large Twist Limit for Any Operator

We argue that for any single-trace operator in ${\cal N}=4$ SYM theory there is a large twist double-scaling limit in which the Feynman graphs have an iterative structure. Such structure can be recast using a graph-building operator. Generically, this operator mixes between single-trace operators with different scaling limits. The mixing captures both the finite coupling spectrum and corrections away from the large twist limit. We first consider a class of short operators with gluons and fermions for which such mixing problems do not arise, and derive their finite coupling spectra. We then focus on a class of long operators with gluons that do mix. We invert their graph-building operator and prove its integrability. The picture that emerges from this work opens the door to a systematic expansion of ${\cal N}=4$ SYM theory around the large twist limit.

hep-th↗

arXiv2021

Mirror channel eigenvectors of the $d$-dimensional fishnets

We present a basis of eigenvectors for the graph building operators acting along the mirror channel of planar fishnet Feynman integrals in $d$-dimensions. The eigenvectors of a fishnet lattice of length $L$ depend on a set of $L$ quantum numbers $(u_k,l_k)$, each associated with the rapidity and bound-state index of a lattice excitation. Each excitation is a particle in $(1+1)$-dimensions with $O(d)$ internal symmetry, and the wave-functions are formally constructed with a set of creation/annihilation operators that satisfy the corresponding Zamolodchikovs-Faddeev algebra. These properties are proved via the representation - new to our knowledge - of the matrix elements of the fused R-matrix with $O(d)$ symmetry as integral operators on the functions of two spacetime points. The spectral decomposition of a fishnet integral we achieved can be applied to the computation of Basso-Dixon integrals in higher dimensions.

hep-th↗

arXiv2020

QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric (fundamental) representations through $r+1$ basic Q-functions. Our functional relations are consistent with the Q-operators proposed recently by one of the authors and verified explicitly on the level of operators at small finite length.

hep-th↗

arXiv2019

Thermodynamic Bethe Ansatz for Fishnet CFT

We present the TBA equations and the Y-system for the exact spectrum of general multi-magnon local operators in the $D$-dimensional anisotropic version of the bi-scalar fishnet CFT. The mixing matrix of such operators is given in terms of fishnet planar graphs of multi-wheel and multi-spiral type. These graphs probe the two main building blocks of the TBA approach that are the magnon dispersion relation and the magnon scattering matrix and which we both obtain by diagonalising suitable graph-building operators. We also obtain the dual version of the TBA equations, which relates, in the continuum limit, $D$-dimensional graphs to two dimensional sigma models in $AdS_{D+1}$. It allows us to verify a general formula obtained by A.~Zamolodchikov for the critical coupling.

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