2017/01/20 by Thomas Creutzig, Creutzig, Thomas · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1701.05926
The Schur-index of the (A1, Xn)-Argyres-Douglas theory is conjecturally a character of a vertex operator algebra. Here such vertex algebras are found for the Aodd and Deven-type Argyres-Douglas theories. The vertex operator algebra corresponding to A2p-3-Argyres-Douglas theory is the logarithmic \mathcal Bp-algebra of [1], while the one corresponding to D2p, denoted by \mathcal Wp, is realized as a non-regular Quantum Hamiltonian reduction of Lk(\mathfrakslp+1) at level k=-(p2-1)/p. For all n one observes that the quantum Hamiltonian reduction of the vertex operator algebra of Dn Argyres-Douglas theory is the vertex operator algebra of An-3 Argyres-Douglas theory. As corollary, one realizes the singlet and triplet algebras (the vertex algebras associated to the best understood logarithmic conformal field theories) as Quantum Hamiltonian reductions as well. Finally, characters of certain modules of these vertex operator algebras and the modular properties of their meromorphic continuations are given.