Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

Afshar H, Creutzig T, Grumiller D, Hikida Y, Rønne PB (2014)

Publication Type: Journal article

Publication year: 2014

Journal

Journal of High Energy Physics Springer Verlag (Germany) / Institute of Physics / Scuola Internazionale Superiore di Studi Avanzati (SISSA)

Book Volume: 2014

Article Number: 63

Journal Issue: 6

DOI: 10.1007/JHEP06(2014)063

Abstract

We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov Wn ²-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n = 2 and n = 4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k + n = (n + 1)/(n - 1). At these points, the Wn ²-algebra is nothing but a compactified free boson. This family of W-algebras admits an 't Hooft limit. Further, in the case of n = 4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product. © 2014 The Author(s).

Involved external institutions

University of Groningen / Rijksuniversiteit Groningen

Netherlands (NL) University of Alberta

Canada (CA) Technische Universität Wien / Vienna University of Technology

Austria (AT) Rikkyo University / 立教大学

Japan (JP) University of Luxembourg

Luxembourg (LU)

How to cite

APA:

Afshar, H., Creutzig, T., Grumiller, D., Hikida, Y., & Rønne, P.B. (2014). Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry. Journal of High Energy Physics, 2014(6). https://doi.org/10.1007/JHEP06(2014)063

MLA:

Afshar, Hamid, et al. "Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry." Journal of High Energy Physics 2014.6 (2014).

BibTeX: Download