Representations of the Nappi--Witten vertex operator algebra
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The Nappi-Witten model is a Wess-Zumino Witten model in which the target space is the nonreductive Heisenberg group $H_4.Abstract:
The Nappi-Witten model is a Wess-Zumino-Witten model in which the target space is the nonreductive Heisenberg group $H_4$. We consider the representation theory underlying this conformal field theory. Specifically, we study the category of weight modules, with finite-dimensional weight spaces, over the associated affine vertex operator algebra $\mathsf{H}_4$. In particular, we classify the irreducible $\mathsf{H}_4$-modules in this category and compute their characters. We moreover observe that this category is nonsemisimple, suggesting that the Nappi-Witten model is a logarithmic conformal field theory.read more
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References
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Weight Representations of Admissible Affine Vertex Algebras
TL;DR: In this paper, a new family of relaxed highest weight representations of affine vertex algebra for affine Kac-Moody algebra of type A was proposed. But these representations are simple quotients of representations of the affine kac-moody matrix.
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PP-waves and logarithmic conformal field theories
TL;DR: In this article, a logarithmic conformal field theory of the coset model SU (2) N/U (1) times a free time-like boson U(1) − N, which admits a spacetime interpretation as a three-dimensional plane wave solution by taking a correlated limit a la Penrose, is presented.
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Realizations of Simple Affine Vertex Algebras and Their Modules: The Cases $${\widehat{sl(2)}}$$ s l ( 2 ) ^ and $${\widehat{osp(1,2)}}$$ o s p ( 1 , 2 ) ^
TL;DR: In this article, the embeddings of simple admissible affine vertex algebras were studied and a family of weight, logarithmic, and Whittaker modules were constructed.
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An admissible level osp (1|2)-model: modular transformations and the Verlinde formula
TL;DR: The modular properties of the simple vertex operator superalgebra associated with the affine Kac-Moody super algebra (1|2) at level −5======¯¯¯¯4 are investigated in this article.
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Weight representations of admissible affine vertex algebras
TL;DR: In this article, a new family of relaxed highest weight representations of affine vertex algebra (V_k(mathfrak{g})$ of type $A) was introduced, which are simple quotients of representations of the affine Kac-Moody algebra.
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