On the ABJ anomaly in the Horava-Lifshitz-like QED
Tiago Mariz, Jose Roberto Nascimento, Albert Yu Petrov · arXiv (Cornell University) · 2015
The Horava-Lifshitz (HL) approach [1, 2], which is characterized by a strong asymmetry between space and time coordinates implying in the presence of different orders in space and time derivatives in the actions of the theories, has been intensively applied not only to HL-like extensions of gravity (for a review see f.e. [3]) but also to the different field theory models whose quantum aspects seem to be much simpler to study. In particular, studies of renormalization and renormalizability of HL-like theories [4], and discussion of different issues related to HL-like extensions of QED [5] should be mentioned. Interesting quantum results were obtained for HL-like extensions of other field theory models, such as CP model [6] and four-fermion model [7]. Also, the effective potential for the HL-like extensions of scalar field models coupled to gauge or spinor fields was obtained for different models (see f.e. [8]). All this certainly calls the interest to study of more sophisticated aspects of the HL-like theories. One of them is just the problem of anomalies, especially the famous Adler-BellJackiw (ABJ) anomaly (triangle anomaly) [9] implying breaking of the chiral symmetry. It is known that just this anomaly causes ambiguities in the theories with “small” Lorentz symmetry breaking [10]. Therefore, it is natural to verify the presence of such anomaly in