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A REALIZATION OF CERTAIN MODULES FOR THE N = 4 SUPERCONFORMAL ALGEBRA AND THE AFFINE LIE ALGEBRA A (1)2

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Abstract

We shall first present an explicit realization of the simple N = 4 superconformal vertex algebra L N = 4 c with central charge c = −9. This vertex superalgebra is realized inside of the bcβγ system and contains a subalgebra isomorphic to the simple affine vertex algebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). Then we construct a functor from the category of L N = 4 c -modules with c = −9 to the category of modules for the admissible affine vertex algebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). By using this construction we construct a family of weight and logarithmic modules for L N = 4 c and L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). We also show that a coset subalgebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \) is a logarithmic extension of the W(2; 3)-algebra with c = −10. We discuss some generalizations of our construction based on the extension of affine vertex algebra L A1 (kΛ 0) such that k + 2 = 1/p and p is a positive integer.

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  1. Department of Mathematics, University of Zagreb, Bijenička 30, 10 000, Zagreb, Croatia

    DRAŽEN ADAMOVIĆ

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ADAMOVIĆ, D. A REALIZATION OF CERTAIN MODULES FOR THE N = 4 SUPERCONFORMAL ALGEBRA AND THE AFFINE LIE ALGEBRA A (1)2 . Transformation Groups 21, 299–327 (2016). https://doi.org/10.1007/s00031-015-9349-2

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