Golterman Maarten, Shamir Yigal
Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA.
Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv, Israel.
Phys Rev Lett. 2024 Feb 23;132(8):081903. doi: 10.1103/PhysRevLett.132.081903.
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.
对称质量产生（SMG）已被倡导为一种在不破坏对称性的情况下使镜像费米子具有质量的机制，其最终目标是构建晶格手征规范理论。有人认为，在SMG相中，镜像费米子传播子中的极点会被零点取代。我们使用有效拉格朗日方法，研究了规范场开启时传播子零点的作用，发现它们表现为耦合的鬼态。在四维中，与正常费米子相比，传播子零点对单圈β函数的贡献符号相反。在二维阿贝尔理论中，传播子零点对光子质量平方有负贡献。此外，传播子零点产生的反常与传播子极点相同。因此，在SMG相中规范不变性将始终得以保持，实际上，即使目标手征规范理论是反常的，但规范理论的幺正性会丧失。
