The \mathfraksu(2)_-1 WZW model

2024/10/16 by Elia Mazzucchelli, Mazzucchelli, Elia
Engineering · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Representation Theory (math.RT) #Superconducting Materials and Applications

paper · pdf · doi:10.48550/arxiv.2410.13017

openalex publication_date 2024/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some WZW models on affine Lie superalgebras at critical level describe string theory on AdS backgrounds at critical values of the string tension. This is the case of \mathfrakpsu(1,1|2)₁ for \rm AdS₃ × \rm S³ and potentially of \mathfraku(2|2)₁ (or related algebras) for \rm AdS₅ × \rm S⁵. Many interesting features of these superalgebra models are already captured by their affine subalgebra \mathfraksu(2)_-1. In this paper we study the WZW model on \mathfraksu(2)_-1: we classify the representations, introduce a free field realisation, and decompose the free field modules in terms of \mathfraksu(2)_-1. We find continuous and discrete modular invariants and see that the latter naturally leads to considering superalgebra extensions of \mathfraksu(2)_-1. Lastly, we find an invariant for the free field theory of four symplectic bosons.

Related

• The \mathfraku(2|2)₁ WZW model
• W-strings from N=2 Hamiltonian reduction and classification of N=2 super W-algebras
• String Theory on AdS(3) Revisited
• Gauged WZNW models and coset constructions in relation to string theories
• An Algorithmic Approach to Operator Product Expansions, W-Algebras and W-Strings