2017/01/31 by Yuan Luo, Meng-Chwan Tan, Petr Vasko +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Boundary (topology) #Dimensional reduction #Duality (order theory) #Homotopy and Cohomology in Algebraic Topology #M-theory #Reduction (mathematics) #Riemann surface #Superpotential #Twist #hep-th
paper · pdf · doi:10.1007/jhep05(2017)121
published in Journal of High Energy Physics 2017(5) (Springer Nature) · 29 pages, minor changes, published version
openalex created_date 2017/02/24 · openalex publication_date 2017/05/01 · arxiv created 2017/05/24 · arxiv updated 2017/05/26 · openalex updated_date 2026/08/05
We perform a series of dimensional reductions of the 6d, N = (2, 0) SCFT on S 2 × Σ × I × S 1 down to 2d on Σ. The reductions are performed in three steps: (i) a reduction on S 1 (accompanied by a topological twist along Σ) leading to a supersymmetric Yang-Mills theory on S 2 × Σ × I, (ii) a further reduction on S 2 resulting in a complex Chern-Simons theory defined on Σ × I, with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of S 2 and S 1, and (iii) a final reduction to the boundary modes of complex Chern-Simons theory with the Nahm pole boundary condition at both ends of the interval I, which gives rise to a complex Toda CFT on the Riemann surface Σ. As the reduction of the 6d theory on Σ would give rise to an N = 2 supersymmetric theory on S 2 × I × S 1, our results imply a 4d-2d duality between four-dimensional N = 2 supersymmetric theory with boundary and two-dimensional complex Toda theory.