arXiv subjects

Enrico Olivucci

Publications and source records attributed to Enrico Olivucci.

17 recordsLinked to original sources

arXiv2026

Provable Quantum-Classical Separation for Continuous Gibbs Sampling

We prove the first quantum-classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-βE}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $α=e^{βΔ}$, where $Δ= \max E-\min E$, every classical algorithm querying the value, gradient, or any higher-order derivatives of the log-density requires $Ω(α)$ queries to sample at constant accuracy in total variation distance, while a quantum algorithm based on quantum singular value thresholding and temperature annealing samples with $\tilde{O}\left(\sqrtα\right)$ queries to an oracle for the gradient. The advantage is quadratic in the barrier amplitude, which becomes exponential in the dimension, $e^{Ω(d)}$, at low temperature. The classical bound is information-theoretic, holding for every classical algorithm with query access to the Gibbs potential and its derivatives at any order.

quant-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

Hexagonalization of Fishnet integrals II: overlaps and multi-point correlators

This work presents the building-blocks of an integrability-based representation for multi-point Fishnet Feynman integrals with any number of loops. Such representation relies on the quantum separation of variables (SoV) of a non-compact spin-chain with symmetry $SO(1,5)$ explained in the first paper of this series. The building-blocks of the SoV representation are overlaps of the wave-functions of the spin-chain excitations inserted along the edges of a triangular tile of Fishnet lattice. The zoology of overlaps is analyzed along with various worked out instances in order to achieve compact formulae for the generic triangular tile. The procedure of assembling the tiles into a Fishnet integral is presented exhaustively. The present analysis describes multi-point correlators with disk topology in the bi-scalar limit of planar $γ$-deformed $\mathcal{N}=4$ SYM theory, and it verifies some conjectural formulae for hexagonalization of Fishnets CFTs present in the literature. The findings of this work are suitable for generalization to a wider class of Feynman diagrams.

hep-th↗

arXiv2023

Multipoint fishnet Feynman diagrams: sequential splitting

We study fishnet Feynman diagrams defined by a certain triangulation of a planar n-gon, with massless scalars propagating along and across the cuts. Our solution theory uses the technique of Separation of Variables, in combination with the theory of symmetric polynomials and Mellin space. The n-point split-ladders are solved by a recursion where all building blocks are made fully explicit. In particular, we find an elegant formula for the coefficient functions of the light-cone leading logs. When the diagram grows into a fishnet, we obtain new results exploiting a Cauchy identity decomposition of the measure over separated variables. This leads to an elementary proof of the Basso-Dixon formula at 4-points, while at n-points it provides a natural OPE-like stratification of the diagram. Finally, we propose an independent approach based on ``stampede" combinatorics to study the light-cone behaviour of the diagrams as the partition function of a certain vertex model.

hep-th↗

arXiv2022

The Loom for General Fishnet CFTs

We propose a broad class of $d$-dimensional conformal field theories of $SU(N)$ adjoint scalar fields generalising the 4$d$ Fishnet CFT (FCFT) discovered by Ö. Gürdogan and one of the authors as a special limit of $γ$-deformed $\mathcal{N}=4$ SYM theory. In the planar $N\to\infty $ limit the FCFTs are dominated by the ``fishnet" planar Feynman graphs. These graphs are explicitly integrable, as was shown long ago by A. Zamolodchikov. The Zamolodchikov's construction, based on the dual Baxter lattice (straight lines on the plane intersecting at arbitrary slopes) and the star-triangle identities, can serve as a ``loom" for ``weaving" the Feynman graphs of these FCFTs, with certain types of propagators, at any $d$. The Baxter lattice with $M$ different slopes and any number of lines parallel to those, generates an FCFT consisting of $M(M-1)$ fields and a certain number of chiral vertices of different valences with distinguished couplings. These non-unitary, logarithmic CFTs enjoy certain reality properties for their spectrum due to a symmetry similar to the PT-invariance of non-hermitian hamiltonians proposed by C. Bender. We discuss in more detail the theories generated by a loom with $M=2,3,4$, and the generalisation of the loom FCFTs for spinning fields in 4$d$.

hep-th↗

arXiv2022

Stampedes II: Null Polygons in Conformal Gauge Theory

We consider correlation functions of single trace operators approaching the cusps of null polygons in a double-scaling limit where so-called $\textit{cusp times}$ $t_i^2 = g^2 \log x_{i-1,i}^2\log x_{i,i+1}^2$ are held fixed and the t'Hooft coupling is small. With the help of stampedes, symbols and educated guesses, we find that any such correlator can be uniquely fixed through a set of coupled lattice PDEs of Toda type with several intriguing novel features. These results hold for most conformal gauge theories with a large number of colours, including planar $\mathcal{N}=4$ SYM.

hep-th↗

arXiv2022

Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges

Some quantities in quantum field theory are dominated by so-called $\mathit{leading\,logs}$ and can be re-summed to all loop orders. In this work we introduce a notion of $\mathit{stampede}$ which is a simple time-evolution of a bunch of particles which start their life in a corner - on the very right say - and $\mathit{hop}$ their way to the opposite corner - on the left - through the repeated action of a quantum Hamiltonian. Such stampedes govern leading logs quantities in certain quantum field theories. The leading euclidean OPE limit of correlation functions in the fishnet theory and null double-scaling limits of correlators in $\mathcal{N}=4$ SYM are notable examples. As an application, we use these results to extend the beautiful bootstrap program of Coronado [1] to all octagons functions with arbitrary diagonal bridge length.

hep-th↗

arXiv2021

Conformal quantum mechanics & the integrable spinning Fishnet

In this paper we consider systems of quantum particles in the $4d$ Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile representations of the principal series $Δ=2+iν$ for any left/right spins $\ell,\dot{\ell}$ of the particles. Such relations are interpreted in the language of Feynman diagrams as integral \emph{star-triangle} identites between propagators of a conformal field theory. We prove the quantum integrability of a spin chain whose $k$-th site hosts a particle in the representation $(Δ_k,\ell_k, \dot{ \ell}_k)$ of the conformal group, realizing a spinning and inhomogeneous version of the quantum magnet used to describe the spectrum of the bi-scalar Fishnet theories. For the special choice of particles in the scalar $(1,0,0)$ and fermionic $(3/2,1,0)$ representation the transfer matrices of the model are Bethe-Salpeter kernels for the double-scaling limit of specific two-point correlators in the $γ$-deformed $\mathcal{N}=4$ and $\mathcal{N}=2$ supersymmetric theories.

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↗

arXiv2021

Hexagonalization of Fishnet integrals I: mirror excitations

In this paper we consider a conformal invariant chain of $L$ sites in the unitary irreducible representations of the group $SO(1,5)$. The $k$-th site of the chain is defined by a scaling dimension $Δ_k$ and spin numbers $\frac{\ell_k}{2}$, $\frac{\dot{\ell}_k}{2}$. The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice "fishnet" integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the $\textit{mirror excitations}$ of the lattice: particles with $SO(4)$ internal symmetry that scatter according to an integrable factorized $\mathcal{S}$-matrix in $(1+1)$ dimensions.

hep-th↗

arXiv2020

Exactly solvable single-trace four point correlators in $χ$CFT$_4$

In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory ($χ$CFT$_4$) arising as a double scaling limit of the $γ$-deformed $\mathcal{N}=4$ SYM theory. In the planar (t'Hooft) limit, each of such correlators is described by a single Feynman integral having the bulk topology of a square lattice "fishnet" and/or of an honeycomb lattice of Yukawa vertices. The computation of this class of Feynmann integrals at any loop is achieved by means of an exactly-solvable spin chain magnet with $SO(1,5)$ symmetry. In this paper we explain in detail the solution of the magnet model as presented in our recent letter and we obtain a general formula for the representation of the Feynman integrals over the spectrum of the separated variables of the magnet, for any number of scalar and fermionic fields in the corresponding correlator. For the particular choice of scalar fields only, our formula reproduces the conjecture of B. Basso and L. Dixon for the fishnet integrals.

hep-th↗

arXiv2020

Exactly solvable magnet of conformal spins in four dimensions

We provide the eigenfunctions for a quantum chain of $N$ conformal spins with nearest-neighbor interaction and open boundary conditions in the irreducible representation of $SO(1,5)$ of scaling dimension $Δ= 2 - i λ$ and spin numbers $\ell=\dot{\ell}=0$. The spectrum of the model is separated into $N$ equal contributions, each dependent on a quantum number $Y_a=[ν_a,n_a]$ which labels a representation of the principal series. The eigenfunctions are orthogonal and we computed the spectral measure by means of a new star-triangle identity. Any portion of a conformal Feynmann diagram with square lattice topology can be represented in terms of separated variables, and we reproduce the all-loop "fishnet" integrals computed by B. Basso and L. Dixon via bootstrap techniques. We conjecture that the proposed eigenfunctions form a complete set and provide a tool for the direct computation of conformal data in the fishnet limit of the supersymmetric $\mathcal{N}=4\,$ Yang-Mills theory at finite order in the coupling, by means of a cutting-and-gluing procedure on the square lattice.

hep-th↗

arXiv2019

Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction

We derive a Hamiltonian structure for the $N$-particle hyperbolic spin Ruijsenaars-Schneider model by means of Poisson reduction of a suitable initial phase space. This phase space is realised as the direct product of the Heisenberg double of a factorisable Lie group with another symplectic manifold that is a certain deformation of the standard canonical relations for $N\ell$ conjugate pairs of dynamical variables. We show that the model enjoys the Poisson-Lie symmetry of the spin group ${\rm GL}_{\ell}({\mathbb C})$ which explains its superintegrability. Our results are obtained in the formalism of the classical $r$-matrix and they are compatible with the recent findings on the different Hamiltonian structure of the model established in the framework of the quasi-Hamiltonian reduction applied to a quasi-Poisson manifold.

hep-th↗

arXiv2019

Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT$_4$

We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT$_4$ proposed by Ö.Gürdoğan and one of the authors as a double scaling limit of $γ$-deformed $\mathcal{N}=4$ SYM theory. We give full description of bulk behavior of large Feynman graphs: it shows a generalized "dynamical fishnet" structure, with a dynamical exchange of bosonic and Yukawa couplings. We compute certain four-point correlators in the full chiral CFT$_4$, generalizing recent results for a particular one-coupling version of this theory -- the bi-scalar "fishnet" CFT. We sum up exactly the corresponding Feynman diagrams, including both bosonic and fermionic loops, by Bethe-Salpeter method. This provides explicit OPE data for various twist-2 operators with spin, showing a rich analytic structure, both in coordinate and coupling spaces.

hep-th↗

arXiv2019

Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model

We conjecture the quantum analogue of the classical trace formulae for the integrals of motion of the quantum hyperbolic Ruijsenaars-Schneider model. This is done by departing from the classical construction where the corresponding model is obtained from the Heisenberg double by the Poisson reduction procedure. We also discuss some algebraic structures associated to the Lax matrix in the classical and quantum theory which arise upon introduction of the spectral parameter.

hep-th↗

arXiv2019

Basso-Dixon Correlators in Two-Dimensional Fishnet CFT

We compute explicitly the two-dimensional version of Basso-Dixon type integrals for the planar four-point correlation functions given by conformal fishnet Feynman graphs. These diagrams are represented by a fragment of a regular square lattice of power-like propagators, arising in the recently proposed integrable bi-scalar fishnet CFT. The formula is derived from first principles, using the formalism of separated variables in integrable SL(2,C) spin chain. It is generalized to anisotropic fishnet, with different powers for propagators in two directions of the lattice.

hep-th↗

arXiv2018

Bi-scalar integrable CFT at any dimension

We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal quantum field theory recently introduced by Gürdogan and one of the authors as a strong-twist double scaling limit of $γ$-deformed $\mathcal{N}=4$ SYM theory. Similarly to the $4D$ case, this D-dimensional CFT is also dominated by "fishnet" Feynman graphs and is integrable in the planar limit. The dynamics of these graphs is described by the integrable conformal $SO(D+1,1)$ spin chain. In $2D$ it is the analogue of L. Lipatov's $SL(2,\mathbb{C})$ spin chain for the Regge limit of $QCD$, but with the spins $s=1/4$ instead of $s=0$. Generalizing recent $4D$ results of Grabner, Gromov, Korchemsky and one of the authors to any $D$ we compute exactly, at any coupling, a four point correlation function, dominated by the simplest fishnet graphs of cylindric topology, and extract from it exact dimensions of R-charge 2 operators with any spin and some of their OPE structure constants.

hep-th↗