arXiv subjects

D. Chicherin

Publications and source records attributed to D. Chicherin.

At least 19 recordsLinked to original sources

arXiv2023

Energy correlations in heavy states

We study energy correlations in states created by a heavy operator acting on the vacuum in a conformal field theory. We argue that the energy correlations in such states exhibit two characteristic regimes as functions of the angular separations between the calorimeters: power-like growth at small angles described by the light-ray OPE and slowly varying, or ``flat'', function at larger angles. The transition between the two regimes is controlled by the scaling dimension of the heavy operator and the dynamics of the theory. We analyze this phenomenon in detail in the planar ${\cal N}=4$ SYM theory both at weak and strong coupling. An analogous transition was previously observed in QCD in the measurement of the angular energy distribution of particles belonging to the same energetic jet. In that case it corresponds to the transition from the light-ray OPE, perturbative regime described in terms of correlations between quarks and gluons to the flat, non-perturbative regime described in terms of correlations between hadrons.

hep-th↗

arXiv2020

All master integrals for three-jet production at NNLO

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in $D$ space-time dimensions. These integrals evaluate to $\mathbb{Q}$-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter, and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless $2\to 3$ scattering process, thereby opening up a new level of precision collider phenomenology.

hep-ph↗

arXiv2020

From correlation functions to event shapes in QCD

We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

hep-th↗

arXiv2019

Analytic form of the full two-loop five-gluon all-plus helicity amplitude

We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude, and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms and rational functions.

hep-ph↗

arXiv2019

Analytic result for a two-loop five-particle amplitude

We compute the symbol of the full-color two-loop five-particle amplitude in $\mathcal{N}=4$ super Yang-Mills, including all non-planar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the non-planar terms, analyze its subleading power corrections, and present analytically the leading logarithmic terms.

hep-th↗

arXiv2019

Analytic result for the nonplanar hexa-box integrals

In this paper, we analytically compute all master integrals for one of the two non-planar integral families for five-particle massless scattering at two loops. We first derive an integral basis of 73 integrals with constant leading singularities. We then construct the system of differential equations satisfied by them, and find that it is in canonical form. The solution space is in agreement with a recent conjecture for the non-planar pentagon alphabet. We fix the boundary constants of the differential equations by exploiting constraints from the absence of unphysical singularities. The solution of the differential equations in the Euclidean region is expressed in terms of iterated integrals. We cross-check the latter against previously known results in the literature, as well as with independent Mellin-Barnes calculations.

hep-ph↗

arXiv2019

The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity

We compute for the first time the two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity. Starting from the known integrand, we perform an integration-by-parts reduction and express the answer in terms of uniform weight master integrals. The latter are known to evaluate to non-planar pentagon functions, described by a 31-letter symbol alphabet. We express the final result for the amplitude in terms of uniform weight four symbols, multiplied by a small set of rational factors. The amplitude satisfies the expected factorization properties when one external graviton becomes soft, and when two external gravitons become collinear. We verify that the soft divergences of the amplitude exponentiate, and extract the finite remainder function. The latter depends on fewer rational factors, and is independent of one of the symbol letters. By analyzing identities involving rational factors and symbols we find a remarkably compact representation in terms of a single seed function, summed over all permutations of external particles. Finally, we work out the multi-Regge limit, and present explicitly the leading logarithmic terms in the limit. The full symbol of the IR-subtracted hard function is provided as an ancillary file.

hep-th↗

arXiv2016

The hyperbolic modular double and the Yang-Baxter equation

We construct a hyperbolic modular double -- an algebra lying in between the Faddeev modular double for $U_q(sl_2)$ and the elliptic modular double. The intertwining operator for this algebra leads to an integral operator solution of the Yang-Baxter equation associated with a generalized Faddeev-Volkov lattice model introduced by the second author. We describe also the L-operator and finite-dimensional R-matrices for this model.

math-ph↗

arXiv2015

New elliptic solutions of the Yang-Baxter equation

We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators reproduce at their bottom the standard Baxter's R-matrix for the 8-vertex model and Sklyanin's L-operator. The general formula has a remarkably compact form and yields new elliptic solutions of the Yang-Baxter equation based on the finite-dimensional representations of the elliptic modular double. The same result is also derived using the fusion formalism.

math-ph↗

arXiv2015

Correlation functions of the chiral stress-tensor multiplet in N=4 SYM

We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.

hep-th↗

arXiv2015

Matrix factorization for solutions of the Yang-Baxter equation

We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the modular double (trigonometric deformation) and the Sklyanin algebra (elliptic deformation). The solutions are matrices with operator entries. The matrix elements are differential operators in the case of sl_2, finite-difference operators with trigonometric coefficients in the case of the modular double or finite-difference operators with coefficients constructed out of Jacobi theta functions in the case of the Sklyanin algebra. We find a new factorized form of the rational, trigonometric, and elliptic solutions, which drastically simplifies them. We show that they are products of several simply organized matrices and obtain for them explicit formulae.

math-ph↗

arXiv2014

Yang-Baxter operators and scattering amplitudes in $\mathcal{N} = 4$ super-Yang-Mills theory

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the extended symmetry and to recover as its consequences many known features like cyclic and inversion symmetry, BCFW recursion, Inverse Soft Limit construction, Grassmannian integral representation, $\mathrm{R}$-invariants and on-shell diagram approach.

hep-th↗

arXiv2013

Yangian symmetric correlators

Similarity transformations and eigenvalue relations of monodromy operators composed of Jordan-Schwinger type L matrices are considered and used to define Yangian symmetric correlators of n-dimensional theories. Explicit expressions are obtained and relations are formulated. In this way basic notions of the Quantum inverse scattering method provide a convenient formulation for high symmetry and integrability not only in lower dimensions.

math-ph↗

arXiv2013

The R-operator for Modular Double

We construct the R-operator -- solution of the Yang-Baxter equation acting in the tensor product of two infinite-dimensional representations of Faddeev's modular double. This R-operator intertwines the product of two L-operators associated with the modular double and it is built from three basic operators generating the permutation group of four parameters S_4.

math-ph↗

arXiv2013

Spinorial R-matrix

R-matrix acting in the tensor product of two spinor representation spaces of Lie algebra so(d) is considered thoroughly. Corresponding Yang-Baxter equation is proved. The relation to the local Yang-Baxter relation is established.

math-ph↗

arXiv2012

Baxter operators with deformed symmetry

Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case.

math-ph↗

arXiv2012

Conformal algebra: R-matrix and star-triangle relation

The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional representations of the conformal algebra and solves Yang-Baxter equation. We build the R-operator as a product of more elementary operators S_1, S_2 and S_3. Operators S_1 and S_3 are identified with intertwining operators of two irreducible representations of the conformal algebra and the operator S_2 is obtained from the intertwining operators S_1 and S_3 by a certain duality transformation. There are star-triangle relations for the basic building blocks S_1, S_2 and S_3 which produce all other relations for the general R-operators. In the case of the conformal algebra of n-dimensional Euclidean space we construct the R-operator for the scalar (spin part is equal to zero) representations and prove that the star-triangle relation is a well known star-triangle relation for propagators of scalar fields. In the special case of the conformal algebra of the 4-dimensional Euclidean space, the R-operator is obtained for more general class of infinite-dimensional (differential) representations with nontrivial spin parts. As a result, for the case of the 4-dimensional Euclidean space, we generalize the scalar star-triangle relation to the most general star-triangle relation for the propagators of particles with arbitrary spins.

math-ph↗

arXiv2011

The Equivalence Theorem in Effective Theories

The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancelation of different groups of contributions.

hep-th↗