Conformal Symmetry and the Chiral Anomaly

Abstract

Two-loop contributions to the anomalous correlation function <J_mu(x)J_nu(y)J_rho(z)> of three chiral currents are calculated by a method based on the conformal properties of massless field theories. The method was previously applied to virtual photon diagrams in quantum electrodynamics, and it is extended here to diagrams with scalars and chiral spinors in the abelian Higgs model and in the SU(3)xSU(2)xU(1) standard model. In each case there are nonvanishing contributions to the gauge current correlator from self-energy insertions, vertex insertions and nonplanar diagrams, but their sum exactly vanishes. The two-loop contribution to the anomaly therefore also vanishes, in agreement with the Adler-Bardeen theorem. An application of the method to the correlator <R_mu(x)R_nu(y)K_rho(z)> of the R and Konishi axial currents in supersymmetric gauge theories which was reported in hep-th/9608125 is discussed here. The net two-loop contribution to this correlator also vanishes.

23 pages, LaTeX, three embedded postscript images

References in corpus (5)

• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• Universality of the Operator Product Expansions of SCFT_4
• Understanding Chiral Anomaly in Coordinate Space
• ON THE HIGHER-LOOP CONTRIBUTIONS TO THE AXIAL ANOMALY
• The radiative corrections of the triangular anomaly

Cited by in corpus (12)

• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Field Theory Tests for Correlators in the AdS/CFT Correspondence
• Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills
• Universality of the Operator Product Expansions of SCFT_4
• Understanding Radiatively Induced Lorentz-CPT Violation in Differential Regularization
• Non-renormalization of two and three Point Correlators of N=4 SYM in N=1 Superspace
• Operator mixing in N=4 SYM: The Konishi anomaly revisited
• Parity-Odd 3-Point Functions from CFT in Momentum Space and the Chiral Anomaly
• Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions
• Conformal Symmetry and the Three Point Function for the Gravitational Axial Anomaly
• Operator mixing in N = 4 SYM: The Konishi anomaly re-re-visited