Gram Matrices for Isotropic Vectors

TL;DR

This paper explores the algebraic structure of Gram matrices with zero diagonal blocks, relevant in quantum field theory, focusing on their determinantal varieties and relations among matrix functions.

Contribution

It introduces a new algebraic framework for analyzing Gram matrices with zero blocks, connecting to conformal correlators in physics.

Findings

Characterization of determinantal varieties for symmetric matrices with zero blocks

Identification of relations among matrix entry functions used in conformal correlators

Application of algebraic geometry to quantum field theory variables

Abstract

We investigate determinantal varieties for symmetric matrices that have zero blocks along the main diagonal. In theoretical physics, these arise as Gram matrices for kinematic variables in quantum field theories. We study the ideals of relations among functions in the matrix entries that serve as building blocks for conformal correlators.