2016/06/30 by Kazunobu Maruyoshi, Junya Yagi
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Brane #Context (archaeology) #Integrable system #Lattice (music) #Quantum many-body systems #Surface (topology) #Transfer matrix #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1093/ptep/ptw151
published as Prog. Theor. Exp. Phys. (2016) 113B01 · 58 pages. v2: minor changes, references added. v3: published version
openalex created_date 2016/06/24 · openalex publication_date 2016/11/01 · arxiv created 2016/12/09 · arxiv updated 2016/12/12 · openalex updated_date 2026/08/05
The supersymmetric index of the 4D <f>N=1</f> theory realized by a brane tiling coincides with the partition function of an integrable 2D lattice model. We argue that a class of half-BPS surface defects in brane tiling models are represented on the lattice model side by transfer matrices constructed from L-operators. For the simplest surface defects in theories with <f>SU(2)</f> flavor groups, we identify the relevant L-operator as that discovered by Sklyanin in the context of the eight-vertex model. We verify this identification by computing the indices of class-<f>S</f> and -<f>Sk</f> theories in the presence of the surface defects.