Propagator Zeros and Lattice Chiral Gauge Theories

Journal Article · 20 February 2024 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.132.081903 · OSTI ID:2310421

Golterman, Maarten ; Shamir, Yigal

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective Lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional Abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: NONE; SC0013682
• OSTI ID: 2310421
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 8 Vol. 132; ISSN 0031-9007; ISSN PRLTAO
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English