Surface Defects and Chiral Algebras

Abstract

We investigate superconformal surface defects in four-dimensional N=2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. In each case we find perfect agreement with the predicted characters.

52 pages, 1 table

References in corpus (7)

• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• R-Twisting and 4d/2d Correspondences
• Vertex operator algebras, Higgs branches, and modular differential equations
• N=1 Deformations and RG Flows of N=2 SCFTs
• Essays on the theory of elliptic hypergeometric functions
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• Chiral Algebras for Trinion Theories

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