相关论文: Hypergeometric representation of a four-loop vacuu…

We derive the first three terms of the epsilon-expansion of the scalar one-loop Bhabha box function from a representation in terms of three generalized hypergeometric functions, which is valid in arbitrary dimensions.

We develop a unitarity method to compute one-loop amplitudes with massless propagators in d=4-2*epsilon dimensions. We compute double cuts of the loop amplitudes via a decomposition into a four-dimensional and a -2*epsilon-dimensional…

We study massive one-loop integrals by analytically continuing the Feynman integral to negative dimensions as advocated by Halliday and Ricotta and developed by Suzuki and Schmidt. We consider n-point one-loop integrals with arbitrary…

A recurrence relation between equal mass two-loop sunrise diagrams differing in dimensionality by 2 is derived and it's solution in terms of Gauss' 2F1 and Appell's F_2 hypergeometric functions is presented. For arbitrary space-time…

The method of dimensional recurrences proposed by one of the authors [1,2] is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result…

We consider the relationship between the higher symmetry and the dynamical decomposition in supersymmetric gauge theory in various dimensions by studying the semi-classical potential energy. We observe that besides the scalar moduli we…

We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…

We continue the effort of defining and evaluating the quantum entropy function for supersymmetric black holes in 4d ${\cal N} = 2$ gauged supergravity, initiated in [1803.05920]. The emphasis here is on the missing steps in the previous…

We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the…

We study the behaviour of an ideal non-relativistic Bose gas in a three-dimensional space where one of the dimensions is compactified to form a circle. In this case there is no phase transition like that for the case of an infinite volume,…

An imaginary part of the false-vacuum energy density in a metastable system, i.e., the decay width due to quantum tunneling, might be reproduced by Borel resummation of vacuum bubble diagrams. We examine the convergence of this prescription…

We introduce a simple algorithm which transforms every four-dimensional cubulation into a cusped finite-volume hyperbolic four-manifold. Combinatorially distinct cubulations give rise to topologically distinct manifolds. Using this…

Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric…

The Coulomb gas partition sum is rewritten in terms of the path integrals formalism. It is shown that perturbation theories based on the Mayer expansion and on the path integrals method lead to the identical results. The well known…

Recently, an asymptotic solution of the Rayleigh equation for an empty bubble in $N$ dimensions has been obtained. Here we give the closed--from general analytical solution of this equation. We also find the general solution of the Rayleigh…

Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.

We consider the scalar sector of a general renormalizable theory and evaluate the effective potential through three loops analytically. We encounter three-loop vacuum bubble diagrams with up to two masses and six lines, which we solve using…

Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…

We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity…

We investigate topology-changing processes in 4-dimensional quantum gravity with a negative cosmological constant. By playing the ``gluing-polytope game" in hyperbolic geometry, we explicitly construct an instanton-like solution without…