W-algebras for Argyres–Douglas theories - Creutzig, Thomas (European Journal of Mathematics, 2017)
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 A2 p - 3-Argyres–Douglas theory is the logarithmic [InlineEquation not available: see fulltext.]-algebra of Creutzig et al. (Lett Math Phys 104(5):553–583, 2014), while the one corresponding to D2 p, denoted by [InlineEquation not available: see fulltext.], is realized as a non-regular quantum Hamiltonian reduction of Lk(slp + 1) at level [InlineEquation not available: see fulltext.]. 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 a 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.
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Keywords: Conformal embeddings; Gauge theories; Logarithmic VOA; W-algebras