What ’ s wrong with anomalous chiral gauge theory ? 1

It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger Model that there is nothing wrong with apparently anomalous chiral gauge theory. If quantised correctly, there should be no gauge anomaly and chiral gauge theory should be renormalisable and unitary, even in higher dimensions and with non-abelian gauge groups. Furthermore, mass terms for gauge bosons and chiral fermions can be generated without spoiling the gauge invariance. Introduction Symmetry has long been an important concept in physics and even broken symmetry is neither less important nor less useful. In particle physics, symmetry is the underlying principle of gauge field theory wherein all fundamental interactions are described. In addition to explicit or spontaneous breaking, quantum fluctuations can also destroy a symmetry which is exact at the classical level. Such breaking was a surprise and hence named anomaly. The well-known anomaly of global axial symmetry is due to the need to regulate short distance singularity of the kind of quantum fluctuations associated with all Feynman loop diagrams [1]. This kind of anomaly has found applications in the phenomenology of neutral pion decays, in the U(1) problem and possibly in the proton spin structure. On the other hand, the anomalous breaking of the local symmetry of a gauge theory is undesirable. It is logically inconsistent if the local gauge invariance which is the underlying principle and also the definition of a gauge theory is lost upon quantisation. Indeed, the inconsistency does show up in the mathematical formulation of anomalous gauge theory. Talk given at the First International Symposium on Symmetries in Subatomic Physics, Taipei, 16-18 May, 1994.