Bi-local Fields in Noncommutative Field Theory

TL;DR

This paper introduces a bi-local representation in noncommutative field theory that simplifies the description of high momentum modes, relates low momentum modes to local fields, and reproduces infrared behaviors of nonplanar diagrams.

Contribution

It presents a novel bi-local framework that connects high and low momentum modes and reproduces key infrared features of noncommutative field theories.

Findings

High momentum modes are described by bi-local fields.

Low momentum modes approximate local fields.

The approach reproduces infrared singularities of nonplanar diagrams.

Abstract

We propose a bi-local representation in noncommutative field theory. It provides a simple description for high momentum degrees of freedom. It also shows that the low momentum modes can be well approximated by ordinary local fields. Long range interactions are generated in the effective action for the lower momentum modes after integrating out the high momentum bi-local fields. The low momentum modes can be represented by diagonal blocks in the matrix model picture and the high momentum bi-local fields correspond to off-diagonal blocks. This block-block interaction picture simply reproduces the infrared singular behaviors of nonplanar diagrams in noncommutative field theory.