A Note on the Non-Commutative Wess-Zumino Model

TL;DR

This paper demonstrates the one-loop renormalizability of the noncommutative Wess-Zumino model with permutation interaction terms and explores the algebraic structure and symmetries of noncommutative field theories.

Contribution

It shows the renormalizability of the NCWZ model at one-loop and derives the algebraic and symmetry properties of noncommutative field theories from Noether currents.

Findings

NCWZ model is renormalizable at one-loop with wave function renormalization.

Logarithmic divergence matches the commutative case when non-commutativity vanishes.

Derived generator algebras and symmetry properties of NCFTs.

Abstract

We show that the noncommutative Wess-Zumino (NCWZ) Lagrangian with permutation terms in the interaction parts is renormalizable at one-loop level by only a wave function renormalization. When the non-commutativity vanishes, the logarithmic divergence of the wave function renormalization of the NCWZ theory is the same as that of the commutative one. Next the algebras of noncommutative field theories (NCFT's) are studied. From Neother currents, the field representation for the generators of NCFT's is extracted. Then based on this representation, the commutation relations between the generators are calculated for NCFT's. The symmetry properties of NCFT's inferred from these commutation relations are discussed and compared with those of the commutative ones.