Related papers: Geometrical methods in loop calculations and the t…
Trigonometry is the study of circular functions, which are functions defined on the unit circle $x^2+y^2 =1$, where distances are measured using the Euclidean norm. When distances are measured using the $L_p$-norm, we get generalized…
The title of this article refers to analytic continuation of three-dimensional Chern-Simons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the volume conjecture, or analytic…
We calculate the four-point function of $1/2$-BPS determinant operators in $\mathcal{N}=4$ SYM at next-to-leading order at weak coupling. We use two complementary methods recently developed for a class of determinant three-point functions:…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their…
Inspired by the recent work of Nima Arkani Hamed and collaborators who introduced the notion of positive geometry to account for the structure of tree-level scattering amplitudes in bi-adjoint $\phi^3$ theory, which led to one-loop…
Conformal 3-point correlators of conserved currents play important roles in numerous directions. These correlators are fixed by conformal symmetry up to a few parameters, which are known only at leading order in perturbative expansions. The…
In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop…
Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent hypergeometric functions $F_4$. In this paper I work out the diagram and…
We use the circle method to count $\mathbb{F}_q(t)$-rational points of bounded naive height on a quadric hypersurface $X\subseteq \mathbb{P}^{n-1}$ defined over $\mathbb{F}_q$, provided that $\mathrm{char}(\mathbb{F}_q)>2$ and $n\ge 3$.…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
Evaluation of three- and four-point diagrams with massless internal particles and arbitrary external momenta is considered. Exact results for some two-loop diagrams (planar and non-planar three-point contributions and the "double box"…
We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold…
For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory…
We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
We correct the computation of one Feynman diagram in the three-loop beta functions for the long-range quartic multi-scalar model, originally presented in (2020 J. Phys. A: Math. Theor. 53 445008) [arXiv:2007.04603]. The correction requires…
We give an algorithm for obtaining expansions of massive two-loop Feynman graphs in powers of the external momentum around a finite, nonzero value of the momentum. This is based on our general two-loop formalism to reduce massive two-loop…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
This article describes the latest versions of the Mathematica packages FeynArts, FormCalc, and LoopTools for the generation and evaluation of one-loop diagrams.
This paper contains an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry. The main tool is a new notion of stable map. We give an outline of a contsruction of…