Vladimir Aleksandrovich Smirnov

Ruthenium-catalyzed reaction of alkyne with vinyl acetate unexpectedly gives 1,4,4-substituted cyclobutene, which can undergo selective thermal ring opening to 1,3-diene and subsequent 1,5-hydrogen shift. The structures of the products were successfully determined by analysis of 1H and 13C NMR spectra using large language models.

We study a five-leg scattering amplitude on the special Coulomb branch of planar N = 4 super Yang-Mills theory. We reach this point of the moduli space of scalar vacuum expectation values by considering six-dimensional N = ( 1 , 1 ) super Yang-Mills theory and reducing it down to four space-time dimensions with extradimensional momenta being nonvanishing. This branch is characterized by massive external W-bosons and massless internal gluons propagating in loops. We analyze the five W-boson amplitude in the kinematics when their masses are much smaller than all Mandelstam-like invariants. This is what we dub the near mass-shell limit. We perform calculations to two-loop order in ’t Hooft coupling, making use of recent advances in analytic calculations of required Feynman integrals. Our findings confirm exponentiation of infrared logarithms and enable us to conjecture a concise all-order expression for the amplitude in question. We further analyze its duality to the square root of a five-point correlation function of infinitely heavy half-BPS (Bogomol’nyi–Prasad–Sommerfield) operators, known as the decagon. By considering the near-null limit for inter-operators distances, we verify that the two objects coincide. This observation corroborates the novel Coulomb amplitudes/heavy correlator duality previously observed for four W-boson amplitudes and Sudakov form factors.

We compute the potential-graviton contributions to the conservative scattering angle of two nonspinning bodies in maximal supergravity at fifth order in Newton’s constant, including second-order self-force effects. Our goal is to tackle the challenging integrals arising at this order in Einstein gravity, but within the technically simpler framework of supergravity. The calculation employs the scattering-amplitude framework, effective field theory, and multiloop integration techniques based on integration by parts and differential equations. The final result is expressed as a series expansion around the static limit, thereby avoiding the explicit evaluation of intricate special functions. This series solution for the master integrals applies, as well, to the corresponding computation in general relativity. Remarkably, we observe nontrivial cancellations among contributions associated with Calabi-Yau integrals, alongside a distinct contribution governed by a Heun differential equation.

Coulomb branch amplitudes of maximally supersymmetric Yang-Mills theory display infrared properties different from their conformal counterparts. While the four-leg amplitude is known to very high perturbative orders, amplitudes of higher multiplicity fall into an uncharted territory starting already from two loops. The reason for this is that they are not easily amenable to traditional techniques like canonical differential equations due to the uncontrolled swelling of solutions to integration-by-parts identities. In this paper, we break the barrier for the five-leg amplitude using a technique based on the analysis of Newton polytopes corresponding to Feynman/Schwinger integrands and their tropical geometry. Specifically, we analytically evaluate the near mass-shell limit of the off-shell pentabox in terms of Goncharov polylogarithms.

We study the multicollinear behavior of tree amplitudes in the six-dimensional N = ( 1 , 1 ) super Yang-Mills theory (sYM). A generalized dimensional reduction of the latter yields the four-dimensional N = 4 sYM on the Coulomb branch, which is of interest for considerations of massive or off-shell scattering. To this end, we revisit the calculation of tree scattering in the former theory employing the collinear bootstrap and known massless limits. Assuming the universality of the double-collinear asymptotics, the result for six-leg superamplitudes differs from the one available in the literature. We further extract the triple-collinear splitting superamplitudes from these.

We present a historiographical review of algorithms and computer codes developed for solving integration-by-parts relations for Feynman integrals. This procedure is one of the key steps in the evaluation of Feynman integrals, since it enables to express integrals belonging to a given family as linear combinations of master integrals. In this review, we restrict ourselves to considering general algorithms which can, in principle, be applied to any family of Feynman integrals. Статья представляет собой историографический обзор алгоритмов и компьютерных программ, разработанных для решения соотношений интегрирования по частям для фейнмановских интегралов. Соответствующая процедура решения является одним из ключевых этапов при вычислении этих интегралов, поскольку позволяет выражать интегралы, принадлежащие заданному семейству, в виде линейных комбинаций мастер-интегралов. В данном обзоре рассматриваются универсальные алгоритмы, которые, в принципе, могут быть применены к любому семейству фейнмановских интегралов.

A bstract: We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase-space integrals without reversed unitarity. We present an Euler integral representation similar to the Lee-Pomeransky representation and explicitly describe a recursive IBP reduction and dimensional shift relations for the general case of n denominators. On the level of master integrals, applying a differential equation approach, we explicitly calculate the previously unknown angular integrals with four denominators for any number of masses to finite order in ε . Extending the idea of dimensional recurrence, we explore the decomposition of angular integrals into branch integrals reducing the number of scales in the master integrals from ( n + 1) n /2 to n + 1. To showcase the potential of this method, we calculate the massless three denominator integral and establish all-order results in ε , including a resummation of soft logarithms.

In this paper, we discuss the factorization of the Sudakov form factor on the Coulomb branch of maximally supersymmetric Yang-Mills theory in the near mass-shell limit. We unravel all pinch singularities of this observable making use of the Method of Regions. We find their operator content in terms of matrix elements of Wilson lines on semi-infinite and finite intervals for the jet and ultrasoft functions, respectively. However, naive factorization into these incoherent momentum components is broken at two-loop order by effects subleading in the parameter of dimensional regularization. To save the day, we perform an appropriate twisting of the functions involved as well as simultaneous finite scheme transformation of the ’t Hooft coupling. Infrared physics of twisted jet and ultrasoft functions is governed by the octagon anomalous dimension, while the untwisted ultrasoft function possesses infrared evolution driven by an anomalous dimension different from the ubiquitous cusp.

We study the form factor of the lowest component of the stress-tensor multiplet away from the origin of the moduli space in the spontaneously broken, aka Coulomb, phase of the maximally supersymmetric Yang-Mills theory for decay into three massive W-bosons. The calculations are done at two-loop order by deriving and solving canonical differential equations in the asymptotical limit of nearly vanishing W-masses. We confirm our previous findings that infrared physics of ‘off-shell observables’ is governed by the octagon anomalous dimension rather than the cusp. In addition, the form factor in question possesses a nontrivial remainder function, which was found to be identical to the massless case, upon a proper subtraction of infrared logarithms (and finite terms). However, the iterative structure of the object is more intricate and is not simply related to the previous orders in coupling as opposed to amplitudes/form factors at the origin of the moduli space.