Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory

TL;DR

This paper constructs a twisted super-Poincaré algebra using Hopf algebra methods to interpret noncommutative quantum field theory as a twisted symmetry, maintaining supersymmetry without breaking it.

Contribution

It introduces a new twist deformation of the super-Poincaré algebra that ensures consistency with non(anti)commutative relations in superspace, preserving supersymmetry.

Findings

The twist deformation is valid for N=1 supersymmetry.

Non(anti)commutative space can be described by a consistent twisted algebra.

Supersymmetry remains unbroken in the twisted framework.

Abstract

In this paper, using a Hopf-algebraic method, we construct deformed Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for N=1 case. We also comment on the possibility of noncommutative central charge coordinate. Finally, because our twist operation does not break the original algebra, we can claim that (twisted) SUSY is not broken in contrast to the string inspired $\mathcal{N}=1/2$ SUSY in N=1 non(anti)commutative superspace.