String states, loops and effective actions in noncommutative field theory and matrix models

TL;DR

This paper develops a formalism using bi-local string states to compute one-loop effective actions in noncommutative field theories and matrix models, revealing stringy features and UV/IR mixing effects.

Contribution

It introduces a coherent state-based approach to analyze loop effects and non-locality in noncommutative geometries, applicable to generic fuzzy spaces and connecting to supergravity.

Findings

Closed-form 1-loop effective action capturing UV/IR mixing

Application to fuzzy spaces and supergravity in IKKT model

String states reveal non-local features of noncommutative theories

Abstract

Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.