Proves maximal transcendentality to all orders for the vacuum-energy expansion of the double-scaled large-N PCM, with coefficients as rational polynomials in odd zeta values after a natural coupling shift.
Mathematical aspects of scattering amplitudes
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abstract
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and discuss introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.
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Computes the leading double logarithm at 5PM in the high-energy gravitational amplitude via multi-H diagrams and dispersion relations, extracting the single-log imaginary part of the eikonal phase.
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
A graph-tubing combinatorial framework governs the first-order differential equations obeyed by master integrals for massive cosmological correlators in de Sitter space.
All-multiplicity building blocks for AdS string amplitudes are defined by dressing flat-space integrals with polylogarithms, yielding derived monodromy relations for open strings and KLT factorization for closed strings.
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.
IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.
Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic computability.
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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.