Modules Over Affine Lie Superalgebras

Abstract

Modules over affine Lie superalgebras $\mathcal{G}$ are studied, in particular, for $\mathcal{G}=\widehat{OSP(1,2)}$. It is shown that on studying Verma modules, much of the results in Kac-Moody algebra can be generalized to the super case. Of most importance are the generalized Kac-Kazhdan formula and the Malikov-Feigin-Fuchs construction, which give the weights and the explicit form of the singular vectors in the Verma module over affine Kac-Moody superalgebras. We have also considered the decomposition of the admissible representation of $\widehat{OSP(1,2)}$ into that of $\widehat{SL(2)}\otimes$Virasoro algebra, through which we get the modular transformations on the torus and the fusion rules. Different boundary conditions on the torus correspond to the different modings of the current superalgebra and characters or super-characters, which might be relevant to the Hamiltonian reduction resulting in Neveu-Schwarz or Ramond superconformal algebras. Finally, the Felder BRST complex, which consists of Wakimoto modules by the free field realization, is constructed.

35 pages

References in corpus (3)

• BRST Analysis of Physical States for 2D (Super) Gravity Coupled to (Super) Conformal Matter
• Physical States in G/G Models and 2d Gravity
• Ground ring for the 2D NSR string

Cited by in corpus (15)

• Free Field Realizations of Affine Current Superalgebras, Screening Currents and Primary Fields
• Cosets, characters and fusion for admissible-level $\mathfrak{osp}(1|2)$ minimal models
• Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case
• Affine sl(2|1) and D(2|1;alpha) as Vertex Operator Extensions of Dual Affine sl(2) Algebras
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Representation theory of the affine Lie superalgebra sl(2|1) at fractional level
• Graded parafermions: standard and quasi-particle bases
• Fusion rules and singular vectors of the osp(1|2) current algebra
• Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
• Structure constants for the osp(1|2) current algebra
• Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modules
• Duality in osp(1|2) Conformal Field Theory and link invariants
• Admissible sl(2/1) Characters and Parafermions
• N-point and higher-genus osp(1|2) fusion
• Parafermionic Representation of the Affine $sl(2/1)$ Algebra at Fractional Level