Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.
复制标题
非酉拉格朗日和酉非拉格朗日共形场论。
DOI：
--
复制
发表时间：
2017
影响因子：
8.6
通讯作者：
Z. Laczko
中科院分区：
文献类型：
--
作者：
M. Buican;Z. Laczko
在不同的维度上，我们有时可以通过计算自由理论中的保护量来计算通过重整化群（RG）流与自由理论相连的相互作用共形场论（cft）的观测值。另一方面，在二维中，通常可以使用自由场以代数方式构造相互作用的cft的可观测值，而无需显式地构造底层RG流。在这封信中，我们开始将这一思想扩展到更高的维度，通过展示人们可以通过执行涉及非幺正自由四维超多重态集的简单计算来计算无限集的幺正强相互作用四维N=2超共形场论（SCFTs）的某些观测值。这些自由场是二维伊辛模型基础上的马约拉纳费米子的远亲，并没有明显地通过RG流与我们的相互作用理论联系起来。令人惊讶的是，这种构造在保留完整的N=2超共形代数的同时，通过牺牲一致性，给出了许多“非拉格朗日”SCFTs的某些子扇区中特定观测量的拉格朗日量。作为一个副产品，我们发现了正仿射Kac-Moody代数和非正仿射Kac-Moody代数中字符之间的关系。我们通过评论我们的构造的可能的概括来结束。
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
非酉量子场论中重正化群流的不可逆性
DOI：
10.1088/1751-8121/aa8a10
发表时间：
2017
期刊：
Mathematical and Theoretical
影响因子：
--
作者：
Castro-Alvaredo O
通讯作者：
Castro-Alvaredo O