Rectangular W-algebras, extended higher spin gravity and dual coset CFTs

Creutzig T, Hikida Y (2019)

Publication Type: Journal article

Publication year: 2019

Journal

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

Book Volume: 2019

Article Number: 147

Journal Issue: 2

DOI: 10.1007/JHEP02(2019)147

Abstract

We analyze the asymptotic symmetry of higher spin gravity with M × M matrix valued fields, which is given by rectangular W-algebras with su(M) symmetry. The matrix valued extension is expected to be useful for the relation between higher spin gravity and string theory. With the truncation of spin as s = 2, 3,…, n, we evaluate the central charge c of the algebra and the level k of the affine currents with finite c, k. For the simplest case with n = 2, we obtain the operator product expansions among generators by requiring their associativity. We conjecture that the symmetry is the same as that of Grassmannian-like coset based on our proposal of higher spin holography. Comparing c, k from the both theories, we obtain the map of parameters. We explicitly construct low spin generators from the coset theory, and, in particular, we reproduce the operator product expansions of the rectangular W-algebra for n = 2. We interpret the map of parameters by decomposing the algebra in the coset description.

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., & Hikida, Y. (2019). Rectangular W-algebras, extended higher spin gravity and dual coset CFTs. Journal of High Energy Physics, 2019(2). https://doi.org/10.1007/JHEP02(2019)147

MLA:

Creutzig, Thomas, and Yasuaki Hikida. "Rectangular W-algebras, extended higher spin gravity and dual coset CFTs." Journal of High Energy Physics 2019.2 (2019).

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