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arXiv · 1602.00278

Anomaly matching condition in two-dimensional systems

O. Dubinkin·A. Gorsky·E. Gubankova
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Abstract

Based on Son-Yamamoto relation obtained for transverse part of triangle axial anomaly in ${\rm QCD}_4$, 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.

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O. Dubinkin, A. Gorsky, E. Gubankova. 2016-01-31. Anomaly matching condition in two-dimensional systems. https://doi.org/10.1103/physrevd.94.085023

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