Related papers: Conformal Triangles and Zig-Zag Diagrams
We develop an operator approach to the evaluation of multiple integrals for multiloop Feynman massless diagrams. A commutative family of graph building operators $H_\alpha$ for ladder diagrams is constructed and investigated. The complete…
We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT$_4$ proposed by \"{O}.G\"{u}rdo\u{g}an and one of the authors as a double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM…
We compute explicitly the two-dimensional version of Basso-Dixon type integrals for the planar four-point correlation functions given by conformal fishnet Feynman graphs. These diagrams are represented by a fragment of a regular square…
We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal quantum field theory recently introduced by G\"{u}rdogan and one of the authors as a strong-twist double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM theory.…
We consider four-point integrals arising in the planar limit of the conformal "fishnet" theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were…
A long-standing conjecture in quantum field theory due to Broadhurst and Kreimer states that the amplitudes of the zig-zag graphs are a certain explicit rational multiple of the odd values of the Riemann zeta function. In this paper we…
We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar $\phi^4$ theory. The results are always multi-linear combinations of ladder integrals, which are in turn built out of classical…
We consider scalar local operators of the determinant type in the conformal ``fishnet'' theory that arises as a limit of gamma-deformed $\mathcal{N}=4$ super Yang-Mills theory. We generalise a field-theory approach to expand their…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B.…
We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed $\mathcal{N}=4$ SYM theory. We show…
We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and…
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…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl…
We compute the leading-color contribution to four-particle scattering amplitude in four-dimensional conformal fishnet theory that arises as a special limit of $\gamma$-deformed $\mathcal N=4$ SYM. We show that the single-trace partial…
In this paper we study a wide class of planar single-trace four point correlators in the chiral conformal field theory ($\chi$CFT$_4$) arising as a double scaling limit of the $\gamma$-deformed $\mathcal{N}=4$ SYM theory. In the planar…
This work presents the building-blocks of an integrability-based representation for multi-point Fishnet Feynman integrals with any number of loops. Such representation relies on the quantum separation of variables (SoV) of a non-compact…
Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four…
Feynman diagrams are a pictorial way of describing integrals predicting possible outcomes of interactions of subatomic particles in the context of quantum field physics. It is highly desirable to have an intrinsic mathematical…