engleski

On recent realizations of simple affine vertex algebras, their applications and generalizations

We shall first review our recent results on explicit free field realizations of affine vertex algebras associated to $\widehat{; ; ; ; sl(2)}; ; ; ; $ and $\widehat{; ; ; ; osp(1, 2}; ; ; ; }; ; ; ; $ and discuss their applications to some open problems in the representation theory of affine vertex algebras. Next we discuss the construction of the $N=4$ superconformal vertex algebra at central charge $c=-9$ which has recently been interpreted in the context of 4d SCFT in physics. We will try to predict which possible generalizations can be expected in the future.

affine vertex algebras ; realizations

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