Misconceptions On Effective Field Theories And Spontaneous Symmetry Breaking Response To Ellis Article
Ellis also states that topological effects, prevalent in low-dimensional condensed matter and solid-state systems such as topological insulators and superconductors, cannot be captured by EFTs because they cannot be derived from a “bottom-up” framework. Again this is incorrect. EFT. On classical grounds, the decay of the neutral pion to two photons is not allowed, but quantum fluctuations allow such a decay through what is called the axial anomaly Bell:1969ts 666A satisfactory description of this anomaly, and its ramifications goes beyond the point of this article, but a nice overview is given in Bertlmann:1996xk for the interested reader. This process is non-local and is captured in an EFT by the Wess-Zumino-Witten (WZW) effective action, first presented in a top-down manner by Wess and Zumino in Wess:1971yu and later derived by Witten Witten:1983tw in a bottom-up fashion Hill:2009wp . This action is topological in nature. POSTSUPERSCRIPT. The WZW formalism for anomaly physics is univ...