A Commutant Realization of 𝒲n(2) at Critical Level

Gao²,

Linshaw³

2012

J. High Energ. Phys.

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The fermionic coset is a limit of the pure spinor formulation of the AdS 5 ×S 5 sigma model as well as a limit of a nonlinear topological A-model, introduced by Berkovits. We study the latter, especially its symmetries, and map them to higher spin algebras.We show the following. The linear A-model possesses affine pgl (4|4) 0 symmetry at critical level and its psl (4|4) 0 current-current perturbation is the nonlinear model. We find that the perturbation preserves W (2) 4 -algebra symmetry at critical level. There is a topological algebra associated to pgl (4|4) 0 with the properties that the perturbation is BRST-exact. Further, the BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the non-trivial generators of the W (2) 4 -algebra. The Zhu functor maps the linear model to a higher spin theory. We analyze its psl (4|4) action and find finite dimensional short multiplets. *

“…As shown in [29], this algebra coincides with the Zhu algebra of W We can also easily realize the algebra pgl (4|4) with the oscillators…”

Section: The Oscillator Algebramentioning

confidence: 71%

Section: -Algebramentioning

confidence: 99%

Section: -Algebramentioning

confidence: 99%

Section: -Algebramentioning

confidence: 99%

Section: -Algebramentioning

confidence: 99%

See 3 more Smart Citations

Fermionic coset, critical level $ \mathcal{W}_4^{{(2)}} $ -algebra and higher spins

Gao²,

Linshaw³

2012

J. High Energ. Phys.

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W-Algebras Extending $$\widehat{\mathfrak{g}\mathfrak{l}}(1\vert 1)$$

Lie Theory and Its Applications in Physics

Ridout

2013

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It was recently shown that gl (1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the operator product algebra are then calculated. Among these extensions, one finds four infinite families that seem to contain, as subalgebras, copies of the W(2) N algebras of Feigin and Semikhatov at various levels and central charges ±1.

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

Afshar

Grumiller

et al. 2014

J. High Energ. Phys.

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We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov W (2) n -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 W (2) n -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.