Correspondences among CFTs with different W-algebra symmetry

Creutzig T, Genra N, Hikida Y, Liu T (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Nuclear Physics B Elsevier

Book Volume: 957

Article Number: 115104

DOI: 10.1016/j.nuclphysb.2020.115104

Abstract

W-algebras are constructed via quantum Hamiltonian reduction associated with a Lie algebra g and an sl(2)-embedding into g. We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. These W-algebras are associated to the same g but distinct sl(2)-embeddings. For this purpose, we first explore different free field realizations of W-algebras and then generalize previous works on the path integral derivation of correspondences of correlation functions. For g=sl(3), there is only one non-standard (non-regular) W-algebra known as the Bershadsky-Polyakov algebra. We examine its free field realizations and derive correlator correspondences involving the WZNW theory of sl(3), the Bershadsky-Polyakov algebra and the principal W3-algebra. There are three non-regular W-algebras associated to g=sl(4). We show that the methods developed for g=sl(3) can be applied straightforwardly. We briefly comment on extensions of our techniques to general g.

Involved external institutions

University of Alberta CA Canada (CA) Kyoto University / 京都大学 Kyōto daigaku JP Japan (JP)

How to cite

APA:

Creutzig, T., Genra, N., Hikida, Y., & Liu, T. (2020). Correspondences among CFTs with different W-algebra symmetry. Nuclear Physics B, 957. https://doi.org/10.1016/j.nuclphysb.2020.115104

MLA:

Creutzig, Thomas, et al. "Correspondences among CFTs with different W-algebra symmetry." Nuclear Physics B 957 (2020).

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