The boundary theory of a spinor field theory on the Bruhat-Tits tree

TL;DR

This paper investigates a spinor field theory on the Bruhat-Tits tree, deriving its boundary action and partition function, revealing a close resemblance to scalar field theories over p-adic numbers.

Contribution

It introduces a novel boundary theory for spinor fields on the Bruhat-Tits tree and computes its action and partition function, highlighting its similarity to p-adic scalar fields.

Findings

Boundary theory closely resembles p-adic scalar field theory

Partition function explicitly computed

Boundary action derived from interior integration

Abstract

For a spinor field theory on the Bruhat-Tits tree, we calculate the action and the partition function of its boundary theory by integrating out the interior of the Bruhat-Tits tree. We found that the boundary theory is very similar to a scalar field theory over p-adic numbers.