arXiv subjects

Andrei A. Pomeransky

Publications and source records attributed to Andrei A. Pomeransky.

8 recordsLinked to original sources

arXiv2025

Monodromy of multiloop integrals in $d$ dimensions

We consider the monodromy group of the differential systems for multiloop integrals. We describe a simple heuristic method to obtain the monodromy matrices as functions of space-time dimension $d$. We observe that in a special basis the elements of these matrices are Laurent polynomials in $z=\exp(iπd)$ with integer coefficients, i.e., the monodromy group is a subgroup of $GL(n,\mathbb{Z}[z,1/z])$. We derive bilinear relations for monodromies in $d$ and $-d$ dimensions which follow from the twisted Riemann bilinear relations and check that the found monodromy matrices satisfy them.

hep-th↗

arXiv2019

Differential equations, recurrence relations, and quadratic constraints for $L$-loop two-point massive tadpoles and propagators

We consider $L$-loop two-point tadpole (watermelon) integral with arbitrary masses, regularized both dimensionally and analytically. We derive differential equation system and recurrence relations (shifts of dimension and denominator powers). Since the $L$-loop sunrise integral corresponds to the $(L+1)$-loop watermelon integral with one cut line, our results are equally applicable to the former. The obtained differential system has a Pfaffian form and is linear in dimension and analytic regularization parameters. In general case, the solutions of this system can be expressed in terms of the Lauricella functions $F_C^{(L)}$ with generic parameters. Therefore, as a by-product, we obtain, to our knowledge for the first time, the Pfaffian system for $F_C^{(L)}$ for arbitrary $L$. The obtained system has no apparent singularities. Near odd dimension and integer denominator powers the system can be easily transformed into canonical form. Using the symmetry properties of the matrix in the right-hand side of the differential system, we obtain quadratic constraints for the expansion of solutions near integer dimension and denominator powers. In particular, we obtain quadratic constraints for Bessel moments similar to those discovered by Broadhurst and Roberts.

hep-ph↗

arXiv2017

Normalized Fuchsian form on Riemann sphere and differential equations for multiloop integrals

We consider the question of reducibility of the differential system to normalized Fuchsian form on the Riemann sphere. The differential equations for the multiloop integrals in $ε$-form constitute a particular example of the normalized Fuchsian form. We formulate the algorithmic criterion of reducibility. We also consider the question of the proper choice of variable in the differential system suitable for its reduction to $ε$-form.

hep-th↗

arXiv2014

General triple charged black ring solution in supergravity

We present the general black ring solution in $U(1)^{3}$ supergravity in 5 dimensions with three independent dipole and electric charges. This immediately gives the general black ring solution in the minimal 5D supergravity as well.

hep-th↗

arXiv2013

Critical points and number of master integrals

We consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the critical points of the polynomials entering either of the two representations: the parametric representation and the Baikov representation. In particular, for the parametric representation the corresponding polynomial is just the sum of Symanzik polynomials. The relevant topological invariant is the sum of the Milnor numbers of the proper critical points. We present a Mathematica package Mint to automatize the counting of the master integrals.

hep-ph↗

arXiv2012

Charged black rings in supergravity with a single non-zero gauge field

General charged black ring solution with two angular momenta, a charge and a dipole charge is found by the inverse scattering method. The solution is presented in a relatively concise form in which its symmetries are manifest. The regularity conditions are found and the physical characteristics of the regular solution are expressed via its parameters.

hep-th↗

arXiv2004

The information entropy of quantum mechanical states

It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently we introduce a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. We derive for it an explicit expression, and discuss some of its general properties. We distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.

quant-ph↗

arXiv2003

Quantum computation of the Anderson transition in presence of imperfections

We propose a quantum algorithm for simulation of the Anderson transition in disordered lattices and study numerically its sensitivity to static imperfections in a quantum computer. In the vicinity of the critical point the algorithm gives a quadratic speedup in computation of diffusion rate and localization length, comparing to the known classical algorithms. We show that the Anderson transition can be detected on quantum computers with $7 - 10$ qubits.

quant-ph↗