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arXiv · 1111.6603

Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins

Thomas Creutzig·Peng Gao·Andrew R. Linshaw
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Abstract

The fermionic coset is a limit of the pure spinor formulation of the AdS5xS5 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 $\AKMSA{pgl}{4}{4}_0$ symmetry at critical level and its $\AKMSA{psl}{4}{4}_0$ current-current perturbation is the nonlinear model. We find that the perturbation preserves $\mathcal{W}^{(2)}_4$-algebra symmetry at critical level. There is a topological algebra associated to $\AKMSA{pgl}{4}{4}_0$ 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 $\mathcal{W}^{(2)}_4$-algebra. The Zhu functor maps the linear model to a higher spin theory. We analyze its $\SLSA{psl}{4}{4}$ action and find finite dimensional short multiplets.

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Thomas Creutzig, Peng Gao, Andrew R. Linshaw. 2011-11-28. Fermionic Coset, Critical Level W^(2)_4-Algebra and Higher Spins. https://doi.org/10.1007/jhep04(2012)031

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