arXiv subjects

Leonid A. Shumilov

Publications and source records attributed to Leonid A. Shumilov.

4 recordsLinked to original sources

arXiv2026

Three-loop anomalous dimensions of leading-twist operators in the Gross-Neveu-Yukawa model

We compute the anomalous dimensions of the leading-twist operators at three-loop level in the $\overline{\text{MS}}$ scheme in the Gross-Neveu-Yukawa model. Calculations are done for a number of low-spin operators using computer algebra systems, and the analytical form is reconstructed by solving a set of Diophantine equations. Calculations are optimized using the emergent supersymmetry of the corresponding generalized theory. For the obtained results, we perform a comprehensive analysis at the critical point, including a comparison with the $1/N$ expansion, a check of the generalized Gribov-Lipatov reciprocity, and an analysis of the behavior next to the rightmost singularity. The latter allows us to extract the values of Regge intercepts for all the leading-twist trajectories in the form of an $ε$ expansion.

hep-th↗

arXiv2026

Graphical Functions by Examples

Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and have enabled major advances, including the highest-loop results currently known in several quantum field theories. Their role extends to conformal field theory, and recent algorithmic developments now allow many graphical functions to be computed automatically. This review, based on graduate-level lectures held by O.S. in 2025/26 at the University of Hamburg, introduces the central ideas behind graphical functions, covering periods, Feynman residues, and the treatment of regular and singular cases in both integer and non-integer dimensions. It also discusses connections to momentum space and self-duality, and provides guidance for further study, offering a coherent entry point into a topic not addressed in standard textbooks.

hep-th↗

arXiv2026

Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing

We calculate the correction exponents in the chiral Heisenberg model in the $1/N$ expansion. These exponents are related to the slopes of $β$ functions at the phase transition point. We present the results at order $1/N^2$ and check that they agree with the results of the $ε$ expansion near $d = 4$. We find that one of the correction exponents diverges as $d \to 3$. We argue that the appearance of the pole is a rather general phenomenon and is associated with operator mixing involving the system of four-fermion operators. After analyzing the operator mixing structure, we propose a resummation procedure which modifies the exponents already at leading order. We also perform calculations directly in the three-dimensional model and find complete agreement with the resummed exponents.

hep-th↗

arXiv2026

Resummation of small-spin singularities in anomalous dimensions of twist-two operators

Anomalous dimensions of leading-twist operators in QCD play an important role in precision predictions for high-energy processes, since they govern the scale evolution of parton distributions. Their analytic structure as a function of spin is particularly important due to the complexity of higher-loop computations. In these proceedings, we discuss the resummation of the certain type of such singularities that share common features with those appearing in the quark flavor-nonsinglet sector of QCD. Our main focus is on the interplay between Gross-Neveu-Yukawa model in $ε$ expansion and Gross-Neveu in $1/N$ expansion. Such resummation allows one to predict the higher-loop singular behavior and reveals connections with the conformal Regge theory and recent studies of detector operators in QCD and various conformal field theories.

hep-th↗