Anomaly matching condition in two-dimensional systems

Abstract

Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in ${\mathrm{QCD}}_4$, we derive its analog in two-dimensional system. It connects the transverse part of mixed vector-axial current two-point function with diagonal vector and axial current two-point functions. Being fully non-perturbative, this relation may be regarded as anomaly matching for conductivities or certain transport coefficients depending on the system. We consider the holographic RG flows in holographic Yang-Mills-Chern-Simons theory via the Hamilton-Jacobi equation with respect to the radial coordinate. Within this holographic model it is found that the RG flows for the following relations are diagonal: Son-Yamamoto relation and the left-right polarization operator. Thus the Son-Yamamoto relation holds at wide range of energy scales.

22 pages, 4 figures

References in corpus (11)

• "Strongly interacting matter in magnetic fields": an overview
• QCD and dimensional deconstruction
• Holographic renormalization as a canonical transformation
• Coulomb drag by small momentum transfer between quantum wires
• Chiral anomalies and AdS/CMT in two dimensions
• The Chiral Magnetic Effect and Axial Anomalies
• On two-point correlation functions in AdS/QCD
• Holography and Anomaly Matching for Resonances
• Holographic two dimensional QCD and Chern-Simons term
• Fermion Pairing and the Scalar Boson of the 2D Conformal Anomaly
• Son-Yamamoto relation and Holographic RG flows