Studies of the Vector-Meson Mass Generation Scheme by Chiral Anomalies in two-Dimensional non-Abelian Gauge Theories

Higher order effects of the two-dimensional non-Abelian gauge theories, in which the vector-meson mass is generated by chiral anomalies, will be studied. The β function and the topological nature of the non-linear σ model in the action and unitarity of the theory will be discussed. Introduction− The fact that chiral symmetry in a Lagrangian at tree level does not survive quantization is well-established, and widely-studied[1], althought we still cannot answer the question whether these anomalies have any physical significance. There are various ways to remove chiral anomaly[2]. Some leads to quite successful prediction[2]. In Jackiw and Rajaraman’s work[3], they adopted an alternative approach. They considered the two-dimensional chiral Schwinger model, and, by simply giving up gauge invariance, obtained a consistent and unitary theory, in which the vector meson necessarily acquires a mass when consistency and unitarity are demanded. R. Rajaraman extended the work to non-Abelian case[6]. At tree level, the nonAbelian chiral Schwinger model is invariant under gauge transformations G, where we can take G as an SU(N) matix without loss of generality. However, the chiral couplings between the gauge fields and fermionic fields will introduce an anomaly. By using the non-Abelian bosonization scheme[4], the anomaly will appear in the bosonized action at its tree level, and the bosonized form of the model is