Trace and Axial Anomalies on Equal Footing

Renata Jora

doi:10.1155/2020/3408734

Abstract

We discussed that for some particular nonsupersymmetric theories, a generalized symmetry that includes both the scale and axial transformations and leads to a single current may contain also a pseudoscalar term. The method, inspired by the superconformal anomalies, has important application for low-energy effective models where it allows the introduction of a single complex glueball field with a scalar and a pseudoscalar component on the same footing with the complex meson nonet fields made of quarks. Both axial and trace anomalies are satisfied in accordance to the meson structure and the QCD requirements.

Highlights

One of the most important tools in dealing with physical systems and especially quantum field theoretical models is the incorporation of symmetries, global or gauged or exact or approximate
The Lagrangian might be scale invariant, at least at tree level, leading to new class of theories whose properties were explored in detail in the literature
The scale invariance is usually broken at the quantum level [1,2,3,4] by the renormalization group equations and at tree level by explicit noninvariant terms in the Lagrangian

Summary

Introduction

One of the most important tools in dealing with physical systems and especially quantum field theoretical models is the incorporation of symmetries, global or gauged or exact or approximate. The effective approach based on the exact realization of axial and scale anomalies for supersymmetric QCD was analyzed by Seiberg [5] and Seiberg and Witten [6] leading to remarkable results regarding the phase structure of these theories. Applications of these methods for QCD were implemented in [7, 8].

Scale Transformation Revisited

Application to a Generalized Linear Sigma Model

Proposal for a Lagrangian Containing a Complex Glueball Field

Conclusions