I discuss the 2-flavor Schwinger model both without and with fermion masses. I argue that the concept 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 $m=e\sqrt{2/π}$, isospin breaking effects in the low energy theory are exponentially suppressed by powers of $\exp\Bigl(-(m/m_f)^{2/3}\Bigr)$ even if $δm\approx m_f$! In the low energy theory, this looks like exponential fine-tuning, but it is done automatically by conformal coalescence.
I discuss the 2-flavor Schwinger model with $θ=0$ and small equal and opposite fermion masses (or $θ=π$ with equal masses). The massless model has an unparticle sector with unbroken conformal symmetry. I argue that this special mass term modifies the conformal sector without breaking the conformal symmetry. I show in detail how mass-perturbation-theory works for correlators of flavor-diagonal fermion scalar bilinears. The result provides quantitative evidence that the theory has no mass gap for small non-zero fermion masses. The massive fermions are bound into conformally invariant unparticle …
On the Correspondence Between the Strongly Coupled 2-Flavor Lattice Schwinger Model and the Heisenberg Antiferromagnetic Chain
利用交错费米子和格点规范理论的哈密顿方法研究了格点上2味无质量Schwinger模型的强耦合极限。利用2味强耦合格点Schwinger模型的低激发态与反铁磁Heisenberg链之间的对应关系，我们用真空期望值（v. e. v.的）的权力海森堡哈密顿量和自旋-自旋关联函数。我们发现一个令人满意的协议与连续理论的结果已经在第二阶强耦合展开。我们表明，图案的对称性破缺的连续介质理论是很好地再现晶格理论，我们确实看到，在晶格理论的isoscillation和isovector手征凝聚体是零到每一个订单的强耦合扩展。此外，我们发现手征凝聚体$<\barψ_{L}^{(2)}\barψ_{L}^{(1)}ψ_{R}^{(1)}ψ_{R}^{(2)}>$在晶格上也是非零的，这是连续介质理论中轴向反常的晶格模型中唯一的遗迹。我们计算出v. e. v.的自旋-自旋耦合子，它们与质量谱的计算有关，并得到了有限大小海森堡哈密顿链的最低态的显式构造。
The two-flavor Schwinger model at 50: Solving Coleman's puzzles
SISSA（国际高等研究学院）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Joseph Henry Laboratories, Princeton University（普林斯顿大学约瑟夫·亨利实验室）；Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论科学中心）
We argue for the quantum-gravitational inconsistency of certain 6d $\mathcal{N}=(1,0)$ supergravity theories, whose anomaly-free gauge algebra $\mathfrak{g}$ and hypermultiplet spectrum $M$ were observed in arxiv:2012.01437 to be realizable only as part of a larger gauge sector $(\mathfrak{g}' \supset \mathfrak{g}, M' \supset M)$ in F-theory. To detach any reference to a string theoretic method of construction, we utilize flavor symmetries to provide compelling reasons why the vast majority of such $(\mathfrak{g},M)$ theories are not compatible with quantum gravity constraints, and how the "au…
