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arXiv · 2307.14608

Smooth modules over the N=1 Bondi-Metzner-Sachs superalgebra

Dong Liu·Yufeng Pei·Limeng Xia·Kaiming Zhao
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Abstract

In this paper, we present a determinant formula for the contravariant form on Verma modules over the N=1 Bondi-Metzner-Sachs (BMS) superalgebra. This formula establishes a necessary and sufficient condition for the irreducibility of the Verma modules. We then introduce and characterize a class of simple smooth modules that generalize both Verma and Whittaker modules over the N=1 BMS superalgebra. We also utilize the Heisenberg-Clifford vertex superalgebra to construct a free field realization for the N=1 BMS superalgebra. This free field realization allows us to obtain a family of natural smooth modules over the N=1 BMS superalgebra, which includes Fock modules and certain Whittaker modules.

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Dong Liu, Yufeng Pei, Limeng Xia, Kaiming Zhao. 2023-07-27. Smooth modules over the N=1 Bondi-Metzner-Sachs superalgebra. https://arxiv.org/abs/2307.14608

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