On skein relations in class S theories

2015/04/01 by Yuji Tachikawa, Tachikawa, Yuji, Noriaki Watanabe +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1504.00121

openalex publication_date 2015/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Loop operators of a class S theory arise from networks on the corresponding Riemann surface, and their operator product expansions are given in terms of the skein relations, that we describe in detail in the case of class S theories of type A. As two applications, we explicitly determine networks corresponding to dyonic loops of N=4 SU(3) super Yang-Mills, and compute the superconformal index of a nontrivial network operator of the T₃ theory.

Related

• Schur indices with class S line operators from networks and further skein relations
• Defect Networks and Supersymmetric Loop Operators
• Line operators in theories of class S, quantized moduli space of flat connections, and Toda field theory
• The superconformal index of theories of class \cal S
• N=1 theories of class S_k