Abstract
We present the vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. As a consequence of the null field construction we determine the degenerate highest weights and prove the corresponding Kac determinant formulae for the conformal ($N=0$) and superconformal ($N=1, 2$) algebras with $N$ supercharges. We also present an explicit construction of spin fields in the $N=1$ oscillator representations of the Neveu–Schwarz and Ramond algebras with extended central charges.
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Digital Object Identifier: 10.2969/aspm/01610205