论文标题
BMS ISING模型的免费现场实现
Free field realization of the BMS Ising model
论文作者
论文摘要
在这项工作中，我们研究了不均匀的BMS自由费用理论，并表明它可以自由地实现BMS Ising模型。我们发现，除了BMS对称性外，在BMS自由费用理论中还存在各向异性缩放对称性。结果，该理论的对称性被增强到由新型的BMS-KAC-MOODY代数产生的无限尺寸对称性，与BMS自由标量模型中的对称性不同。除了$ u（1）$ kac-moody电流与BMS代数的不同耦合外，Kac-Moody级别现在不变，因此相应的模块进一步扩大到BMS-KAC-KAC-KAC-MOODY交错模块。我们表明，在电流的运营商产品扩展中存在基本的$ W（2,2,1）$结构，并且可以将BMS-KAC-kac-Moody交错模块视为此$ W $ - 代数的最高重量模块。此外，我们通过Fermion-Boson二元性获得BMS ISING模型。对于BMS $ _3 $，该BMS ISING模型不是最小模型，因为基于BMS KAC的最小模型构建始终会导致手性virasoro最小模型。取而代之的是，BMS ISING模型的基本代数是$ W（2,2,1）$ - 代数，可以理解为量子共形BMS $ _3 $代数。
In this work, we study the inhomogeneous BMS free fermion theory, and show that it gives a free field realization of the BMS Ising model. We find that besides the BMS symmetry there exists an anisotropic scaling symmetry in BMS free fermion theory. As a result, the symmetry of the theory gets enhanced to an infinite dimensional symmetry generated by a new type of BMS-Kac-Moody algebra, different from the one found in the BMS free scalar model. Besides the different coupling of the $u(1)$ Kac-Moody current to the BMS algebra, the Kac-Moody level is nonvanishing now such that the corresponding modules are further enlarged to BMS-Kac-Moody staggered modules. We show that there exists an underlying $W(2,2,1)$ structure in the operator product expansion of the currents, and the BMS-Kac-Moody staggered modules can be viewed as highest-weight modules of this $W$-algebra. Moreover we obtain the BMS Ising model by a fermion-boson duality. This BMS Ising model is not a minimal model with respect to BMS$_3$, since the minimal model construction based on BMS Kac determinant always leads to chiral Virasoro minimal models. Instead, the underlying algebra of the BMS Ising model is the $W(2,2,1)$-algebra, which can be understood as a quantum conformal BMS$_3$ algebra.
