23 problems

Let a $(3,n)$ generalized Feynman diagram (GFD) be a combinatorial object compatible with color orderings in the sense of the paper. Compatibility-count conjecture. Every $(3,n)$ G…

Let $\Gamma_{L^\ast}$ be a graph in the class of loop BCFW graphs $\mathbf{\Gamma}^{\mathtt{BCFW}}_{k,n;L^\ast}$, and let … be the corresponding branch of the loop BCFW recursion.…

Let $\mathcal{A}^{(3),\sigma}_n$ be a generic, pure generalized nonlinear sigma model $3$-amplitude, and consider any single soft limit obtained by sending one external kinematic d…

Flavour-background quotient conjecture. Collinear singularities in this theory are given by the quotient of $\mathcal{A}^{N,K}_{\mathrm{Defect}}$ by the relation that sets all bulk…

Yang–Mills scattering form conjecture. The $(2n-4)$-form $\Upsilon_n$ coincides with the $\mathcal{N}=4$ SYM scattering form defined by HZ.

Non-crossing chord diagram conjecture. The regions contributing to $A_n^{\phi^4}$ are in bijection with the $C_{n/2-1}$ possible non-crossing chord diagrams. The region associated w…

Let $n$ be even, let $x=(x_0,cldots,x_{n-3})cincmathbb{R}^{n-2}$, and define … A non-crossing chord diagram is a perfect matching of $n-2$ ordered points, with chords $ctheta_{ab}$…

Fundamental decoupling identity. Fix a fundamental triple $\mathcal{T}=(\Sigma_0,\Sigma_1,\Sigma_2)$. As $\Sigma\in CO(k,n)$ ranges over all double $\mathcal{T}$-extensions…

Block-partition factorization conjecture. There is an ordering $(\mathbf{T}_1,\ldots,\mathbf{T}_{(d-1)(k-1)-1},\mathbf{S})$ with…

Three-ary factorization conjecture. To leading order in these three parameters,

Place $n-2$ points labeled $0,1,\ldots,n-3$ in increasing order on the real line, and let $H(x)$ be the function in the global Schwinger formula for $A^{\phi^p}_n$. For a non-cross…

Residue reduction conjecture. The $(k-2)(n-k-2)$-dimensional residue of $m^{(k)}_n$ on the subspace where $\eta_J=0$ for every $\eta_J\in\text{base}_{k,n}\cup\text{comb}_{k,n}$ can…

Let $k\geq 1$ and $n\geq k+4$. Let $\mathcal{A}_{n,k,4}$ be the amplituhedron, and let $\mathcal{BCFW}_{n,k}$ denote the collection of $4k$-dimensional BCFW positroid cells in the…

Resolved amplitude conjecture. There exists a set of linear functions $\hat{\eta}_J(s)$ such that

Bern–Carrasco–Johansson colour–kinematics duality conjecture. There exists a choice of kinematic numerators for the trivalent diagrams entering $\scA_{n,L}$ such that whenever a tr…

Let $\mathcal{K}(k,n)$ be the kinematic space, let $J\in\binom{[n]}{k}^{\mathrm{nf}}$, and define … where $(i,j)\in[1,k-1]\times[1,n-k+1]$. For $\alpha\in\mathbb{R}^{(k-1)(n-k+1)}$…

For integers satisfying $k e 0$ and $k+m e n$, let $Z$ be a totally positive matrix and let $\mathcal{A}{n,k,m}(Z)$ be the image of $mathop{rm Gr}+(k,n)$ under the induced map. A po…

Let an LS function determine a combinatoric polytope obtained from its associated scattering-form or kinematic-space construction. Simplicity conjecture. All combinatoric polytopes…

Let $\mathcal{W}(k,n)$ be the cell complex associated to admissible Wilson loop diagrams with $k$ propagators on $n$ vertices. Let $B$ be a cell of dimension $3k-1$, let $W$ and…

Let $Z\in\operatorname{Mat}_{k+4,n}^{>0}$, and let $\mathcal{C}_{n,k,4}$ be the collection of BCFW cells in $\operatorname{Gr}_{k,n}^{\geq 0}$. Arkani-Hamed–Trnka triangulation con…

Let ${\mathcal A}(k,n,m;l^L)$ be an Amplituhedron, let $\Delta^D$ have positive coordinates $X_1,\ldots,X_D$, and let … be a morphism from positive coordinates to the Amplituhedron…

A master integral is one of the finitely many basis integrals to which the integrals of a topology reduce through integration-by-parts identities. A master integral is uniformly tr…

Consider an $L$-loop amplitude in dimensional regularisation with $D=4-2\epsilon$, and write its Laurent expansion in $\epsilon$. Maximum-transcendentality conjecture. The Laurent c…