论文标题
较高的排名f z二
Higher rank FZZ-dualities
论文作者
论文摘要
我们通过概括了Fateev-Zamolodchikov-Zamolodchikov（fzz-）对$ \ Mathfrak {SL}（SL}（2）/\ Mathfrak {U}（1）$ coset-liieville和Sine-lii的理论，我们提出了二维形式形式的二元性二元性（FZE-Zamolodchikov-Zamolodchikov（fzz-）双重性，提出了新的强/弱对偶性。在先前的工作中，通过将减少方法从$ \ mathfrak {sl}（2）$ wess-zumino-novikov-witten模型应用于liouville田间理论和liouville田间理论的自我二元性来提供。在本文中，我们与类型的$ \ Mathfrak {sl}（n+1）/（\ Mathfrak {sl}（n）\ Times \ Times \ Mathfrak {U}（1））$合作，并提出该模型与$ \ \ Mathfrak {sl}（n+1 | n）$结构对理论是双词。我们通过在$ \ m athfrak {sl}（n）$上应用最新的作品以及Toda字段理论的自dualtion，以$ n = 2,3 $明确地得出双重性。我们的结果可以被视为Gaiotto-rapčák角角点顶点操作员代数$ y_ {0，n，n，n，n+1} [ψ] $和$ y_ {n，0，n，0，n+1} [ψ^{ - 1}] $。
We propose new strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten's cigar model described by the $\mathfrak{sl}(2)/\mathfrak{u}(1)$ coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from $\mathfrak{sl}(2)$ Wess-Zumino-Novikov-Witten model to Liouville field theory and the self-duality of Liouville field theory. In this paper, we work with the coset model of the type $\mathfrak{sl}(N+1)/(\mathfrak{sl}(N) \times \mathfrak{u}(1))$ and propose that the model is dual to a theory with an $\mathfrak{sl}(N+1|N)$ structure. We derive the duality explicitly for $N=2,3$ by applying recent works on the reduction method extended for $\mathfrak{sl}(N)$ and the self-duality of Toda field theory. Our results can be regarded as a conformal field theoretic derivation of the duality of the Gaiotto-Rapčák corner vertex operator algebras $Y_{0, N, N+1}[ψ]$ and $Y_{N, 0, N+1}[ψ^{-1}]$.
