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On free field realization of the twisted Heisenberg-Virasoro algebra at level zero and W-algebra W(2,2)

We present a free field realisation of the Heisenberg-Virasoro VOA and it's highest weight modules. As an application we derive intertwining operators among irreducible highest weight modules. We show the existence of non-split self-extensions. In the end we discuss applications to W(2, 2) algebra.

vertex algebras, Heisenberg-Virasoro algebra, screening operators, intertwining operators

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