论文标题

无质量施温格模型的四弗斯特象变形

Four-fermion deformations of the massless Schwinger model and confinement

论文作者

Cherman, Aleksey, Jacobson, Theodore, Shifman, Mikhail, Unsal, Mithat, Vainshtein, Arkady

论文摘要

我们考虑无数的电荷-N $ schwinger型号及其与两个四弗里尔操作员的变形。没有变形,该模型表现出手性对称性的破坏而无需限制。通常断言,无质量的舒温格模型总是被剥离,并且只有在打开费米昂的质量时才会出现弦张力。我们表明,在这些四个特里米昂操作员的存在下,无数理论实际上可以局限于局限。四个特里米昂变形之一是手性中性的,是边缘变形。另一个操作员可以是相关的或无关紧要的,并且尊重$ \ mathbb {z} _2 $的手性对称性,甚至$ n $,因此禁止质量术语。当它相关时,即使是完全无质量的理论也会表现出限制和自发性手性对称性破裂。该结构类似于2d中的QCD(adj)。尽管没有四个特性变形的理论被解剖,但具有这些变形的理论通常在狭窄的阶段。我们使用持续化研究了$ \ mathbb {r}^2 $上的模型,还分析了$ \ mathbb {r} \ times s^1 $上的限制机制,在这里我们发现限制是由分数instantons驱动的。

We consider the massless charge-$N$ Schwinger model and its deformation with two four-fermion operators. Without the deformations, this model exhibits chiral symmetry breaking without confinement. It is usually asserted that the massless Schwinger model is always deconfined and a string tension emerges only when a mass for the fermion field is turned on. We show that in the presence of these four-fermion operators, the massless theory can in fact confine. One of the four-fermion deformations is chirally neutral, and is a marginal deformation. The other operator can be relevant or irrelevant, and respects a $\mathbb{Z}_2$ subgroup of chiral symmetry for even $N$, hence forbidding a mass term. When it is relevant, even the exactly massless theory exhibits both confinement and spontaneous chiral symmetry breaking. The construction is analogous to QCD(adj) in 2d. While the theory without four-fermion deformations is deconfined, the theory with these deformations is generically in a confining phase. We study the model on $\mathbb{R}^2$ using bosonization, and also analyze the mechanism of confinement on $\mathbb{R}\times S^1$, where we find that confinement is driven by fractional instantons.

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