String modes, propagators and loops on fuzzy spaces

TL;DR

This paper introduces a systematic way to organize functions and operators on fuzzy spaces using string modes, simplifying quantum field theory calculations and clarifying nonlocal effects like UV/IR mixing.

Contribution

It presents a novel organization of functions on fuzzy spaces that separates semi-classical and quantum regimes, facilitating loop computations and understanding nonlocality.

Findings

Simplifies loop calculations on fuzzy spaces

Provides direct position space effective action

Clarifies UV/IR mixing as nonlocality from string modes

Abstract

We present a systematic organization of functions and operators on the fuzzy 2-sphere in terms of string modes, which are optimally localized in position and momentum space. This allows to separate the semi-classical and the deep quantum regime of non-commutative quantum field theory and exhibits its nonlocal nature. This organization greatly simplifies the computation of loop contributions, avoiding oscillatory integrals and providing the effective action directly in position space. UV/IR mixing is understood as nonlocality arising from long string modes in the loops. The method is suited for any quantized symplectic space.