对数共形场论的原型关系
Relating the Archetypes of Logarithmic Conformal Field Theory
摘要：
对数共形场论是现代数学物理的一个丰富而充满活力的领域，它在凝聚态理论和弦论中都有著名的应用。我们对这些理论的有限理解是基于对各种例子的详细研究，这些例子可以被视为原型。这些模型包括c=-2三重态模型、SL（2;R）上k=-1/2水平的Wess-Zumino-Witten模型及其GL（1）上的超群类似物|1）。在这里，后者的模型进行了研究代数通过表示理论，融合和模块化的不变性，促进其陪集和扩展代数的后续调查。结果表明，对数共形场论的原型实际上都是非常密切相关的，许多其他例子也是如此，特别是SL（2| 1）1级和-1/2级的模型。因此，结论是，对数共形场论的原型例子实际上都是一样的，所以我们不应该期望它们的特征在任何方面都是通用的。必须寻找更多的原型例子。
英文摘要：
Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal. These include the c=-2 triplet model, the Wess-Zumino-Witten model on SL(2;R) at level k=-1/2, and its supergroup analogue on GL(1|1). Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras. The results show that the archetypes of logarithmic conformal field theory are in fact all very closely related, as are many other examples including, in particular, the SL(2|1) models at levels 1 and -1/2. The conclusion is then that the archetypal examples of logarithmic conformal field theory are practically all the same, so we should not expect that their features are in any way generic. Further archetypal examples must be sought.
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