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

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. Keywords: Anti-de Sitter/conformal field theory correspondence, Gauge/gravity correspondence, p-adic number, Spinor field, Bruhat-Tits tree