Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
Graphical functions and single-valued multiple polylogarithms
8 Pith papers cite this work. Polarity classification is still indexing.
8
Pith papers citing it
abstract
Graphical functions are single-valued complex functions which arise from Feynman amplitudes. We study their properties and use their connection to multiple polylogarithms to calculate Feynman periods. For the zig-zag and two more families of phi^4 periods we give exact results modulo products. These periods are proved to be expressible as integer linear combinations of single-valued multiple polylogarithms evaluated at one. For the larger family of 'constructible' graphs we give an algorithm that allows one to calculate their periods by computer algebra. The theory of graphical functions is used to prove the zig-zag conjecture.
citation-role summary
background 3
method 1
citation-polarity summary
fields
hep-th 8representative citing papers
Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
Four-loop four-point correlator integrand in planar N=4 SYM decomposes into chamber forms identical to three loops times local integrands, with leading singularities as linear combinations of those forms and a diagonalized pure-function representation including one pure elliptic integrand.
Four-loop anomalous dimensions of φ^Q in scalar-QED are obtained via OPE, with beta functions and mass/field anomalous dimensions, validating OPE beyond pure scalar theories.
Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.
citing papers explorer
-
Deriving motivic coactions and single-valued maps at genus zero from zeta generators
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
-
Fano and Reflexive Polytopes from Feynman Integrals
Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.
-
Towards Motivic Coactions at Genus One from Zeta Generators
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
-
Leading singularities and chambers of Correlahedron
Four-loop four-point correlator integrand in planar N=4 SYM decomposes into chamber forms identical to three loops times local integrands, with leading singularities as linear combinations of those forms and a diagonalized pure-function representation including one pure elliptic integrand.
-
Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion
Four-loop anomalous dimensions of φ^Q in scalar-QED are obtained via OPE, with beta functions and mass/field anomalous dimensions, validating OPE beyond pure scalar theories.
-
A thermal representation for conformal ladder integrals
Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.
- Graphical Functions by Examples
- The OPE Approach to Renormalization: Operator Mixing