78 problems

Let $G$ be a subdivergence-free graph with $n$ loops, let $I^{\mathrm{res}}_G$ denote its Feynman residue, and let $Z_n$ be the zig-zag graph with $n$ loops. Hepp's zig-zag graph c…

Let $G$ be a graph that is p-logarithmic in $d=4$ dimensions and whose vertices all have degree at most $4$; call such a graph a $\phi^4$ graph. Let $\mathcal{P}(G)$ denote its per…

Henn's conjecture. There always exists a rotation into a basis $\boldsymbol{J}(\boldsymbol{x},\varepsilon)$ in which the master integrals satisfy an $\varepsilon$-factorized differ…

Let the classical polylogarithms be defined by … and let … be the multiple polylogarithm appearing in the claim. Duhr's conjecture. All multiple polylogarithms of weight at most…

Let an ideal be Cohen–Macaulay when its depth equals its Krull dimension. Associate to a Feynman integral the ideal generated by the relevant polynomials or data defining its Feynm…

A Feynman integral is an integral arising from a perturbative quantum field theory amplitude, and a hypergeometric function in the general sense is a function belonging to the broa…

Magic-relation conjecture. A sector produces a magic relation if and only if its critical variety has a higher-dimensional component.

Let $f_{\overline{G}_8}(z)$ be the irreducible internally completed graphical function in four dimensions associated with the graph $\overline{G}_8$, with all edges of weight $1$.…

Generation conjecture. The holonomic $\mathcal{D}$-ideal of rank $2^{\ell+1}-1$ for the $\ell$-loop banana integral is generated by these $\ell+3$ operators.

A generalized polylogarithm (GPL) is defined iteratively by … with $G(;x)=1$ and $G(\vec{0}_n;x)=\frac{1}{n!}\ln^n(x)$. Its transcendentality is its weight, namely the number of it…

Let $R_m=\mathbb{C}(s_1,\ldots,s_m)\langle \partial_1,\ldots,\partial_m\rangle$ be the rational Weyl algebra, and let $\mathcal{I}$ be the left ideal generated by…

Let $\tau$ be a scalar quantum field theory on $\mathbb{R}^d$, let $G$ be a Feynman graph of the theory, and let $A_G$ denote its multivariate regularised Feynman rules, with regul…

Comodule conjecture. Primitive Feynman integrals are conjectured to form a comodule under the motivic Galois coaction.

For each loop order $L$, consider the period Feynman integrals of $\phi^4$ theory and sample them with probability inversely proportional to the symmetry factor of their associated…

Flat-space partial-fraction decomposition conjecture. The flat-space wavefunction can be decomposed into partial fractions as

Restricted GKZ singular-locus conjecture. The singular locus of a restricted GKZ system arising from a Feynman integral coincides with the Euler discriminant.

Let $G$ be a primitive graph, let $\omega^{4k+1}$ denote a primitive form of the indicated degree, and let the canonical integral and the Rossi–Willwacher integral be the correspon…

Let ${\tt A}_n$ be the one-loop diagram with $n$ external legs and $n$ internal edges, and let ${\cal E}^{(0,0)}$ be the kinematic subspace where both internal and external masses…

PLD containment conjecture. For any Feynman diagram $G$ and any linear subspace ${\cal E}\subseteq{\cal K}$,

For an $n$-loop banana amplitude in dimension $D=2$ with generic masses, let $\operatorname{ord}(n)$ denote the order of its Picard–Fuchs equation. Lairez's order conjecture. The o…

Let $\hat{E}_t^{(n)}$ be the Fourier-transformed differential operator associated with the $n$-loop banana amplitude, and let $\widehat{PF}^{(n)}_{t}$ be its Picard–Fuchs different…

The universal $\varepsilon$-factorisation conjecture. A transformation to an $\varepsilon$-factorised form can be found for all Feynman integrals.

Brown's subdivided-edge invariance conjecture. This morphism factors through the quotient by the relation $G\sim G'$ whenever $G'$ is obtained from $G$ by subdividing an edge.

Let $X_{(3,1,4);4}$ be the pentabox hypersurface in projective space, let $\omega_{(3,1,4);4}$ be the algebraic differential form defining the corresponding Feynman integral, and l…

A unimodular triangulation is a triangulation of the relevant Feynman configuration or its associated lattice polytope into simplices that are unimodular with respect to the ambien…