Poincar\'e Invariant Quantum Field Theories With Twisted Internal Symmetries

TL;DR

This paper develops Poincaré invariant quantum field theories with twisted internal symmetries, introducing nonlocal quantum fields that still allow for local, Lorentz-invariant interactions, simplifying certain supersymmetric theory deformations.

Contribution

It constructs a new class of quantum field theories with twisted internal symmetries that maintain Lorentz invariance and locality at the interaction level, despite nonlocal field commutation relations.

Findings

Twisted quantum fields satisfy nonstandard commutation relations.

Local interaction Hamiltonians can be constructed despite nonlocal fields.

Twisted symmetries simplify the analysis of eformations in supersymmetric theories.

Abstract

Following up the work of [1] on deformed algebras, we present a class of Poincar\'e invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct local interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can significantly simplify the discussion of the marginal deformations (\beta-deformations) of the N=4 SUSY theories.