Conformal anomaly of pseudo-scalar operators

Abstract

We study the conformal properties of pseudo-scalar (parity-odd) operators in four-dimensional field theory. Such operators include the topological term in a gauge theory and the Yukawa coupling. We show that a single operator of this type cannot be a conformal primary on its own. This is only possible for certain mixtures of pseudo-scalar operators like the chiral Lagrangian of $\mathcal{N}=4$ super-Yang-Mills theory. We examine the detailed mechanism of conformal symmetry breakdown and derive an anomalous conformal Ward identity. We explore a possible link between this conformal anomaly and the axial anomaly.

arXiv comment17 pages, 3 figures

References in corpus (8)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• The Uses of Conformal Symmetry in QCD
• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• Three-Loop Four-Point Correlator in N=4 SYM
• The super-correlator/super-amplitude duality: Part I
• From correlation functions to scattering amplitudes
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM