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The N = 1 super Heisenberg–Virasoro vertex algebra at level zero

We study the representation theory of the 𝑁=1 super Heisenberg– Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg–Virasoro vertex algebra [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg– Virasoro algebra at level zero and its applications, J. Pure Appl. Algebra219(10) (2015) 4322–4342 ; D. Adamović and G. Radobolja, Self-dual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero, Commun. Contemp. Math.21(2) (2019) 1850008 ; Y. Billig, Representations of the twisted Heisenberg– Virasoro algebra at level zero, Can. Math. Bull.46(4) (2003) 529–537] to the super case. We calculated all characters of irreducible highest weight representations by investigating certain Fock space representations. Quite surprisingly, we found that the maximal submodules of certain Verma modules are generated by subsingular vectors. The formulas for singular and subsingular vectors are obtained using screening operators appearing in a study of certain logarithmic vertex algebras [D. Adamović and A. Milas, On W- algebras associated to (2, 𝑝) minimal models and their representations, Int. Math. Res. Notices2010(20) (2010) 3896–3934].

Super Heisenberg–Virasoro vertex algebra

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