Unified $(p,q; α,γ, l)$-deformation of oscillator algebra and two-dimensional conformal field theory

Abstract: The unified $ (p,q; \alpha,\gamma, l)$-deformation of a number of well-known deformed oscillator algebras is introduced.The deformation is constructed by imputing new free parameters into the structure functions and by generalizing the defining relations of these algebras. The generalized Jordan-Schwinger and Holstein-Primakoff realizations of the $U_{pq}^{\alpha \gamma l}(su(2))$ algebra by the generalized $ (p,q; \alpha,\gamma, l)$-deformed operators are found. The generalized $ (p,q; \alpha,\gamma, l)$-deformation of the two-dimensional conformal field theory is established. By introducing the $ (p,q; \alpha,\gamma, l)$-operator product expansion (OPE) between the energy momentum tensor and primary fields, we obtain the $ (p,q; \alpha,\gamma, l)$-deformed centerless Virasoro algebra. The two-point correlation function of the primary generalized $ (p,q; \alpha,\gamma, l)$-deformed fields is calculated.