Motivic Gerasimov–Shatashvili amplitude conjecture

Let $A_{\mathbb{Q}_p}^{(N)}(\boldsymbol{s})$ be the $p$-adic Koba–Nielsen amplitudes, and let $A_{\mathbb{C((}T\mathbb{))}}^{(N)}(\boldsymbol{L})$ denote the motivic string amplitudes over $\mathbb{C((}T\mathbb{))}$. Their specialization at $\boldsymbol{L}=p$ gives the $p$-adic amplitudes, while specialization at $\boldsymbol{L}=1$ gives the Denef–Loeser amplitudes. Let $A_{GS}^{(N)}$ denote the Feynman amplitudes of the Gerasimov–Shatashvili Lagrangian at the motivic, or “three”, level. Motivic Gerasimov–Shatashvili conjecture. The Feynman amplitudes at the three level of the Gerasimov–Shatashvili Lagrangian are related to

$$\lim_{p\rightarrow1}A_{\mathbb{Q}_p}^{(N)}(\boldsymbol{s}).$$

The paper reports verification for the four- and five-point amplitudes, while the general statement remains conjectural; the wording “are by related” is reproduced mathematically as an unspecified relation.