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Journal Articles Nuclear Physics B Year : 2016

The continuum limit of a (2) N −1 spin chains


Building on our previous work for a (2) 2 and a (2) 3 we explore systematically the continuum limit of gapless a (2) N −1 vertex models and spin chains. We find the existence of three possible regimes. Regimes I and II for a (2) 2n−1 are related with a (2) 2n−1 Toda, and described by n compact bosons. Regime I for a (2) 2n is related with a (2) 2n Toda and involves n compact bosons, while regime II is related instead with B (1) (0, n) super Toda, and involves in addition a single Majorana fermion. The most interesting is regime III, where non-compact degrees of freedom appear, generalising the emergence of the Euclidean black hole CFT in the a (2) 2 case. For a (2) 2n we find a continuum limit made of n compact and n non-compact bosons, while for a (2) 2n−1 we find n compact and n − 1 non-compact bosons. We also find deep relations between a (2) N−1 in regime III and the gauged WZW models SO(N)/SO(N − 1).
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Dates and versions

hal-01393299 , version 1 (07-11-2016)





Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur. The continuum limit of a (2) N −1 spin chains. Nuclear Physics B, 2016, 911, pp.52-93. ⟨10.1016/j.nuclphysb.2016.07.026⟩. ⟨hal-01393299⟩
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