Null Fields Realizations of $W_3$ from $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ Algebras

Abstract

We consider the nonlinear algebras $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct realizations modulo null fields of the $W_3$ algebra that lies in the cosets $W(sl(4),sl(3))/u(1)$ and $W(sl(3|1),sl(3))/u(1)$. Such realizations exist for the following values of the $W_3$ algebra central charge: $c_W=-30,-40/7,-98/5,-2$. The first two values are listed for the first time, whereas for the remaining values we get the new realizations in terms of an arbitrary stress tensor and $u(1)\times sl(2)$ affine currents.

Submitted to Phys. Lett. B; PACS-no 11.30.Ly

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Cited by in corpus (3)

• Thermodynamic Geometry and Hawking Radiation
• Effective gravity and OSp(N,4) invariant matter
• The W(sl(N+3),sl(3)) algebras and their contractions to W3