\sigma-regularity of the vertex superalgebra L_{c_m}

Abstract:

Let $L_{c_m}$ be the irreducible vertex superalgebra constructed by the N=2 superconformal algebra with $c_m=\frac{3m}{m+2}$. Drazen Adamovic gave the proof of the regularity of L_{c_m} in 2001.We consider the simple vertex superalgebra L_{c_{m}} and the automorphism \sigma, which satisfy \sigma|_{(L_{c_m})_{\bar0}}=id and \sigma|_{(L_{c_m})_{\bar1}}=-id. We give the proof of the \sigma-regularity of L_{c_{m}}.