On $p$-adic string amplitudes in the limit $p$ approaches to one

Understand

In this article we discuss the limit $p$ approaches to one of tree-level $p$-adic open string amplitudes and its connections with the topological zeta functions.

• There is empirical evidence that $p$-adic strings are related to the ordinary strings in the $p \to 1$ limit.
• Previously, we established that $p$-adic Koba-Nielsen string amplitudes are finite sums of multivariate Igusa's local zeta functions, consequently, they are convergent integrals that admit meromorphic continuations as rational functions.
• The meromorphic continuation of local zeta functions has been used for several authors to regularize parametric Feynman amplitudes in field and string theories.