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FZZ-triality and large N=4 super Liouville theory

Creutzig, Thomas Hikida, Yasuaki 京都大学 DOI:10.1016/j.nuclphysb.2022.115734

2022.04

概要

We examine dualities of two dimensional conformal field theories by applying the methods developed in previous works. We first derive the duality between SL(2|1)k/(SL(2)k ⊗ U (1)) coset and Witten's cigar model or sine-Liouville theory. The latter two models are Fateev-Zamolodchikov-Zamolodchikov (FZZ-)dual to each other, hence the relation of the three models is named FZZ-triality. These results are used to study correlator correspondences between large N = 4 super Liouville theory and a coset of the form Y (k1, k2)/SL(2)k1+k2, where Y (k1, k2) consists of two SL(2|1)ki and free bosons or equivalently two U (1) cosets of D(2, 1; ki − 1) at level one. These correspondences are a main result of this paper. The FZZ-triality acts as a seed of the correspondence, which in particular implies a hidden SL(2)k′ in SL(2|1)k or D(2, 1; k − 1)₁. The relation of levels is k′ − 1 = 1/(k − 1). We also construct boundary actions in sine-Liouville theory as another use of the FZZ-triality. Furthermore, we generalize the FZZ-triality to the case with SL(n|1)k/(SL(n)k ⊗ U (1)) for arbitrary n > 2.

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