Towards Non-archimedean Superstrings

TL;DR

This paper proposes a $p$-adic superstring action on a Minkowski space, establishing supersymmetry, deriving amplitudes, and comparing them to prior $p$-adic superstring results, advancing non-archimedean string theory.

Contribution

It introduces a novel $p$-adic superstring action with supersymmetry and computes explicit tree-level amplitudes, extending the understanding of non-archimedean string models.

Findings

Constructed a $p$-adic superstring action with supersymmetry.

Derived explicit four-point amplitudes and a Koba-Nielsen formula.

Compared new amplitudes with previous $p$-adic superstring results.

Abstract

An action for a prospect of a $p$-adic open superstring on a target Minkowski space is proposed. The action is constructed for `worldsheet' fields taking values in the $p$-adic field $\mathbb{Q}_p$, but it is assumed to be obtained from a discrete action on the Bruhat-Tits tree. This action is proven to have an analog of worldsheet supersymmetry and the superspace action is also constructed in terms of superfields. The action does not have conformal symmetry, however it is implemented in the definition of the amplitudes. The tree-level amplitudes for this theory are obtained for $N$ vertex operators corresponding to tachyon superfields and a Koba-Nielsen formula is obtained. Finally, four-point amplitudes are computed explicitly and they are compared to previous work on $p$-adic superstring amplitudes.