Georgi Howard
Center for the Fundamental Laws of Nature, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev Lett. 2020 Oct 30;125(18):181601. doi: 10.1103/PhysRevLett.125.181601.
I discuss the two-flavor Schwinger model both without and with fermion masses. I argue that the phenomenon of "conformal coalescence," in unparticle physics in which linear combinations of short-distance operators can disappear from the long-distance theory, makes it easy to understand some puzzling features of the model with small fermion masses. In particular, I argue that for an average fermion mass m_{f} and a mass difference δm, so long as both are small compared to the dynamical gauge boson mass m=esqrt[2/π], isospin-breaking effects in the low-energy theory are exponentially suppressed by powers of exp[-(m/m_{f})^{2/3}] even if δm≈m_{f}. In the low-energy theory, this looks like exponential fine-tuning, but it is done automatically by conformal coalescence.
我讨论了无费米子质量和有费米子质量的两味施温格模型。我认为，在单粒子物理中，短程算符的线性组合可能会从长程理论中消失的“共形合并”现象，使得我们能够轻松理解具有小费米子质量的模型的一些令人困惑的特征。具体而言，我认为对于平均费米子质量(m_f)和质量差(\delta m)，只要它们与动态规范玻色子质量(m = e\sqrt{2/\pi})相比都很小，那么即使(\delta m \approx m_f)，低能理论中的同位旋破缺效应也会被(\exp[-(m/m_f)^{2/3}])的幂次指数抑制。在低能理论中，这看起来像是指数微调，但它是由共形合并自动完成的。
