论文标题
自二u（1）晶格场理论，具有$θ$ - term
Self-dual U(1) lattice field theory with a $θ$-term
论文作者
论文摘要
我们以修改的反派行动研究U（1）仪表理论。这样的理论自然可以与电气和磁性物质耦合，并显示出精确的电磁偶性。在他们最简单的配方中，没有$θ$ - 期，这些理论是超本地的。我们将讨论扩展到使用$θ$ terms的U（1）量学理论，使得$θ$周期性对于自由理论来说是确切的，并表明施加电力磁性二元性会导致当地但不是超局部的晶格动作，这让人联想到lüscher的轴向构造构造轴向对齐的固定式固定式固定型。我们讨论了与电气和磁性物质以及底子的耦合。对于二代物质，$θ$ - 角（$2π$）的电磁二重性和$2π$的变化会产生sl $（2，\ mathbb z）$二元转换组，就像在连续体中一样。我们最终说明了SL $（2，\ Mathbb z）$二元性如何用于探索有限$θ$的理论，而不会出现标志问题。
We study U(1) gauge theories with a modified Villain action. Such theories can naturally be coupled to electric and magnetic matter, and display exact electric-magnetic duality. In their simplest formulation without a $θ$-term, such theories are ultra-local. We extend the discussion to U(1) gauge theories with $θ$-terms, such that $θ$ periodicity is exact for a free theory, and show that imposing electric-magnetic duality results in a local, but not ultra-local lattice action, which is reminiscent of the Lüscher construction of axial-symmetry preserving fermions in 4d. We discuss the coupling to electric and magnetic matter as well as to dyons. For dyonic matter the electric-magnetic duality and shifts of the $θ$-angle by $2π$ together generate an SL$(2,\mathbb Z)$ duality group of transformations, just like in the continuum. We finally illustrate how the SL$(2,\mathbb Z)$ duality may be used to explore theories at finite $θ$ without a sign problem.
