The N=2,4 supersymmetric linear W∞[λ] algebras for generic λ parameter

초록

The four different kinds of currents are given by the multiple (beta,gamma) and (b,c) ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation parameter lambda appearing in the conformal weights of above fields nontrivially and depend on the generic spinsh 1 and h(2) appearing on the left hand sides in the (anti)commutators. By taking the linear combinations of these currents, the N= 4 supersymmetric linear W infinity[lambda] algebra (and its N= 4 super-space description) for generic lambda is obtained explicitly. Moreover, we determine the N= 2 supersymmetric linear W-infinity[ lambda] algebra for arbitrary lambda. As a by product, the lambda deformed bosonic W1+infinity[lambda]xW(1+infinity)[lambda+12] subalgebra (a generalization of Pope, Romans and Shen's work in1990) is obtained. The first factor is realized by(b,c) fermionic fields while the second factor is realized by (beta,gamma) bosonic fields. The degrees of the polynomials in lambda forthe structure constants are given by( h(1+)h(2)-2). Each w(1+infinity )algebra from the celestial holography is reproduced by taking the vanishing limit of other deformation prameter q at lambda= 0 with the contractions of the currents.

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