Recursion Relations in $p$-adic Mellin Space

Understand

In this work, we formulate a set of rules for writing down $p$-adic Mellin amplitudes at tree-level.

• The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams.
• The prescription is recursive in nature, with two different physical interpretations: one as a recursion on the number of internal lines in the diagram, and the other as reminiscent of on-shell BCFW recursion for flat-space amplitudes, especially when viewed in auxiliary momentum space.
• The prescriptions are proven in full generality, and their close connection with Feynman rules for real Mellin amplitudes is explained.