Poincare' Quasi-Hopf Symmetry and Non-Associative Spacetime Algebra from Twisted Gauge Theories

TL;DR

This paper explores how twisted gauge theories on non-commutative spacetimes reveal an underlying Poincaré quasi-Hopf symmetry algebra, leading to a non-associative spacetime algebra, with implications for formulating gauge theories without extra degrees of freedom.

Contribution

It demonstrates that gauge theories on twisted non-commutative spacetimes possess a Poincaré quasi-Hopf symmetry, establishing a non-associative spacetime algebra framework.

Findings

Gauge theories can be formulated without new gauge degrees of freedom.

The underlying symmetry algebra is identified as Poincaré quasi-Hopf.

The resulting spacetime algebra is non-associative.

Abstract

In previous work, starting from the Moyal plane, we formulated interacting theories of matter and gauge fields with only the former fields twisted. In this approach, gauge theories, including the standard model, can be formulated without new gauge degrees of freedom. We show their underlying symmetry algebra to be Poincar\'e quasi-Hopf . The associated spacetime algebra is hence non-associative.