Naslov
On the N=1 super Heisenberg-Virasoro vertex algebra
(On the 𝑁=1 super Heisenberg-Virasoro vertex algebra)

Autori
Adamović, Dražen ; Jandrić, Berislav ; Radobolja, Gordan

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Lie Groups, Number Theory, and Vertex Algebras

Urednik/ci
Adamović, Dražen ; Dujella, Andrej ; Milas, Antun ; Pandžić, Pavle

Izdavač
American Mathematical Society (AMS)

Godina
2021

Raspon stranica
167-178

ISBN
978-1-4704-5351-0

Ključne riječi
Heisenberg-Virasoro super algebra, vertex algebra

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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