Nonassociative Field Theory on Non-Geometric Spaces

TL;DR

This paper develops a formalism for nonassociative field theories on non-geometric spaces using quasi-Hopf twist deformations, analyzing their impact on Feynman diagrams and providing explicit calculations for phi(4) theory.

Contribution

It introduces a novel approach to construct perturbative nonassociative field theories on non-geometric backgrounds using cochain twist deformations.

Findings

Modified classification of Feynman diagrams into planar and non-planar

Explicit one-loop calculations for phi(4) theory on non-geometric space

Demonstration of nonassociative deformations affecting quantum field theory

Abstract

We describe quasi-Hopf twist deformations of flat closed string compactifications with non-geometric R-flux using a suitable cochain twist, and construct nonassociative deformations of fields and differential calculus. We report on our new findings in using this formalism to construct perturbative nonassociative field theories on these backgrounds. We describe the modifications to the usual classification of Feynman diagrams into planar and non-planar graphs. The example of phi(4) theory is studied in detail and the one-loop contributions to the two-point function are calculated.