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On the 𝑁=1 super Heisenberg-Virasoro vertex algebra

We introduce the N = 1 super Heisenberg-Virasoro vertex algebra V^SH(c_L, c_α, c_{; ; L, α}; ; ), which is a super-analog of the Heisenberg- Virasoro vertexalgebra. We also define the N = 1 super Heisenberg- Virasoro conformal algebra, so that V^SH(c_L, c_α, c_{; ; L, α}; ; ) is its universal enveloping vertex algebra. We show that when c_α is nonzero, the simple vertex algebra V^SH(c_L, c_α, c_{; ; L, α}; ; ) is isomorphic to the tensor product of Clifford- Heisenberg vertex algebra and simple N = 1 Neveu-Schwarz vertex algebra of suitable central charge. This generalises results from [1]. In the case of level zero, i.e, c_α = 0, we also find a free-field realization which generalises the realisation from [3]. In our forthcoming paper, we shall study the representation theory of V^SH(c_L, c_α=0, c_{; ; L, α}; ; ) at level zero.

Heisenberg-Virasoro super algebra, vertex algebra

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