Global Symmetries and Renormalizability of Lee-Wick Theories

TL;DR

This paper investigates the global symmetries and renormalizability of Lee-Wick scalar QED, demonstrating finiteness of divergences and computing one-loop beta-functions, highlighting differences from ordinary scalar QED.

Contribution

It identifies softly broken SO(1,1) symmetries in Lee-Wick theories and shows how these symmetries constrain renormalization and divergence structure.

Findings

Finiteness of superficially divergent amplitudes in LW Abelian gauge theory

Explicit one-loop renormalization demonstrating symmetry constraints

Computed one-loop beta-functions contrasting with ordinary scalar QED

Abstract

In this paper we discuss the global symmetries and the renormalizibility of Lee-Wick scalar QED. In particular, in the "auxiliary-field" formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1) invariant gauge-fixing conditions that allow us to show in the two-field formalism directly that the number of superficially divergent amplitudes in a LW Abelian gauge theory is finite. To illustrate the renormalizability of the theory, we explicitly carry out the one-loop renormalization program in LW scalar QED and demonstrate how the counterterms required are constrained by the joint conditions of gauge- and SO(1,1)-invariance. We also compute the one-loop beta-functions in LW scalar QED and contrast them with those of ordinary scalar QED.