7 problems

In the on-shell formalism, let $\mathcal{P}$ be the algebra of local polynomials and let $\mathcal{W}\subset\mathcal{P}$ be an $SL2\mathbb{C}$-invariant representative of the Wick…

Let $G$ be a compact simple group of rank $r$, let \textit{\text{\boldmathvarphi}} denote angular variables on a maximal Abelian torus, and let \textit{\text{\boldmathchi…

Ward-identity conjecture. The Ward identity, in the sense of van Nieuwenhuizen and Schnitzer (2022), holds in both cases when restricting to the graphs of maximal order of divergen…

Generalized Ward identity conjecture. The Ward identities for $Z_n^{(m)}$ are

Graviton density-family conjecture. The perturbative expansion with respect to $\mathfrak{h}^{\{\omega\}}_{\mu\nu}$ depends on $\omega$ only through the external-leg structure. Con…

Let $n\geq 5$ and consider stringy on-shell Ward identities associated with the $SL(K+3,\mathbb{C})$ symmetry. The nonlinear Ward identities are obtained through the reduction of s…

Let $\phi_\alpha(x):=\phi(x)e^{i\alpha(x)}$, $\phi^*_\alpha(x):=\phi^*(x)e^{-i\alpha(x)}$, and, for a local functional $F$, let $F_\alpha:=F(\phi_\alpha,\phi^*_\alpha,A^\mu)$, wher…