Large-c superconformal torus blocks

We study large-c SCFT2 on a torus specializing to one-point superblocks in the N = 1 Neveu-Schwarz sector. Considering different contractions of the Neveu-Schwarz superalgebra related to the large central charge limit we explicitly calculate three superblocks, osp(1 vertical bar 2) global, light, and heavy-light superblocks, and show that they are related to each other. We formulate the osp(1 vertical bar 2) superCasimir eigenvalue equations and identify their particular solutions as the global superblocks. It is shown that the resulting differential equations are the Heun equations. We study exponentiated global superblocks arising at large conformal dimensions and demonstrate that in the leading approximation the osp(1 vertical bar 2) superblocks are equal to the non-supersymmetric sl(2) block.