A precise mapping from the world-sheet integral of the AdS Virasoro-Shapiro amplitude to the energy-energy correlator in strongly coupled N=4 SYM, with explicit flat-space and first curvature correction terms.
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Multiple polylogarithms and mixed Tate motives
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abstract
We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives over a ring of integers in a number field. Describe explicitly the multiple polylogarithm Hopf algebra.
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representative citing papers
Noncommutative twisted de Rham theory derives the intersection number of open-string contours whose inverse is the double-copy kernel for four-point AdS string generating functions.
Introduces Goncharov Lie coalgebra from GL homology and uses it with spectral sequences to describe rational K-theory of fields via weight-3 polylogarithms beyond prior low-degree cases.
Constructs a graphical coaction for all-loop FRW integrals in conformally-coupled scalar theories via twisted (co)homology, with combinatorial description of kinematic flow and a public web app for computation.
Constructs motivic local systems for one-loop graphs in momentum space whose weight-graded pieces are Tate twists of quadratic Artin motives from maximally cut quotient graphs, along with a formula for the de Rham motivic Galois group action.
In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
An explicit Galois descent formula expresses multiple t-values of maximal height as linear combinations of multiple zeta values via iterated beta integrals, with applications to multiple zeta-half values.
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
Proposes a conjectural invariance under anti-automorphism for a functional on admissible words in iterated q-integrals with position-dependent shifts, as q-analogue of duality on P1 minus four points.
Single-valued polylogarithms are constructed on higher-genus once-punctured Riemann surfaces with trivial monodromy, related to prior work and used to identify the Arakelov Green's function.
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.
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
A generating series is derived for the sum of multiple zeta values ending with a fixed string, implying the sum has depth bounded by the sum of the string entries.
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.
citing papers explorer
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Energy-Energy Correlator from the AdS Virasoro-Shapiro Amplitude
A precise mapping from the world-sheet integral of the AdS Virasoro-Shapiro amplitude to the energy-energy correlator in strongly coupled N=4 SYM, with explicit flat-space and first curvature correction terms.
-
Twisted de Rham theory for string double copy in AdS
Noncommutative twisted de Rham theory derives the intersection number of open-string contours whose inverse is the double-copy kernel for four-point AdS string generating functions.
-
The Goncharov Lie coalgebra of a field
Introduces Goncharov Lie coalgebra from GL homology and uses it with spectral sequences to describe rational K-theory of fields via weight-3 polylogarithms beyond prior low-degree cases.
-
A Graphical Coaction for FRW Integrals from Partial/Relative Twisted (Co)homology
Constructs a graphical coaction for all-loop FRW integrals in conformally-coupled scalar theories via twisted (co)homology, with combinatorial description of kinematic flow and a public web app for computation.
-
Motivic Galois theory for one-loop Feynman integrals in momentum space
Constructs motivic local systems for one-loop graphs in momentum space whose weight-graded pieces are Tate twists of quadratic Artin motives from maximally cut quotient graphs, along with a formula for the de Rham motivic Galois group action.
-
Walking Sudakov: From Cusp to Octagon
In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
-
A construction of single-valued elliptic polylogarithms
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
-
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.
-
An explicit Galois descent for multiple $t$-values of maximal height
An explicit Galois descent formula expresses multiple t-values of maximal height as linear combinations of multiple zeta values via iterated beta integrals, with applications to multiple zeta-half values.
-
All-loop four-quark Bethe-Salpeter kernel
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
-
Conjectural duality for iterated $q$-integrals on $\mathbb{P}^{1}$ minus four generic points
Proposes a conjectural invariance under anti-automorphism for a functional on admissible words in iterated q-integrals with position-dependent shifts, as q-analogue of duality on P1 minus four points.
-
Single-valued polylogarithms for higher genera
Single-valued polylogarithms are constructed on higher-genus once-punctured Riemann surfaces with trivial monodromy, related to prior work and used to identify the Arakelov Green's function.
-
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.
-
Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
-
Multiple zeta values ending with a fixed string
A generating series is derived for the sum of multiple zeta values ending with a fixed string, implying the sum has depth bounded by the sum of the string entries.
-
Genus drop involving non-hyperelliptic curves in Feynman integrals
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.