On Free Field Realizations of $W(2,2)$-Modules

Abstract

The aim of the paper is to study modules for the twisted Heisenberg-Virasoro algebra $\mathcal{H}$ at level zero as modules for the $W(2,2)$-algebra by using construction from [J. Pure Appl. Algebra 219 (2015), 4322-4342, arXiv:1405.1707]. We prove that the irreducible highest weight $\mathcal{H}$-module is irreducible as $W(2,2)$-module if and only if it has a typical highest weight. Finally, we construct a screening operator acting on the Heisenberg-Virasoro vertex algebra whose kernel is exactly $W(2,2)$ vertex algebra.

several presentational changes made and misprints corrected

References in corpus (3)

• Logarithmic intertwining operators and W(2,2p-1)-algebras
• Classification of Harish-Chandra modules over the $W$-algebra W(2,2)
• W-algebra W(2,2) and the vertex operator algebra L(1/2,0)\otimes L(1/2,0)

Cited by in corpus (7)

• The (super)conformal BMS${}_3$ algebra
• Galilean contractions of $W$-algebras
• Higher-order Galilean contractions
• The BRST quantisation of chiral BMS-like field theories
• Multi-graded Galilean conformal algebras
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• Galilean $W_3$ algebra