2007/06/30 by Erich Poppitz, Yanwen Shang
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-lat #hep-th
paper · pdf · doi:10.1088/1126-6708/2007/08/081
published as JHEP0708:081,2007 · 29 pages, 2 figures; published version, new addendum
openalex publication_date 2007/08/28 · arxiv created 2007/09/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We show, using exact lattice chirality, that partition functions of lattice gauge theories with vectorlike fermion representations can be split into "light" and "mirror" parts, such that the "light" and "mirror" representations are chiral. The splitting of the full partition function into "light" and "mirror" is well defined only if the two sectors are separately anomaly free. We show that only then is the generating functional, and hence the spectrum, of the mirror theory a smooth function of the gauge field background. This explains how ideas to use additional non-gauge, high-scale mirror-sector dynamics to decouple the mirror fermions without breaking the gauge symmetry--for example, in symmetric phases at strong mirror Yukawa coupling--are forced to respect the anomaly-free condition when combined with the exact lattice chiral symmetry. Our results also explain a paradox posed by a recent numerical study of the mirror-fermion spectrum in a toy would-be-anomalous two-dimensional theory. In passing, we prove some general properties of the partition functions of arbitrary chiral theories on the lattice that should be of interest for further studies in this field.