Conformal Triangles and Zig-Zag Diagrams

Abstract

A convenient integral representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional fishnet field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. In particular, we give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag multi-loop two-point diagrams which make a significant contribution to the renormalization group beta-function in 4-dimensional phi^4 theory.

References in corpus (17)

• Implications of Conformal Invariance in Field Theories for General Dimensions
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Numbers and Functions in Quantum Field Theory
• Knots and Numbers in ${\varphi }^4$ Theory to 7 Loops and Beyond
• Gluing Ladders into Fishnets
• Strongly γ-deformed N=4 SYM as an integrable CFT
• Multi-loop Feynman integrals and conformal quantum mechanics
• Bi-scalar integrable CFT at any dimension
• Six loop analytical calculation of the field anomalous dimension and the critical exponent $\eta$ in $O(n)$-symmetric ${\phi }^4$ model
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• Exactly solvable magnet of conformal spins in four dimensions
• Generalised ladders and single-valued polylogarithms
• Operator approach to analytical evaluation of Feynman diagrams

Cited by in corpus (3)

• Recursive computation of Feynman periods
• Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
• Checkerboard CFT