The Witten index of the (2, 0)-theory compactified on spaces of the form S^3/ΓxS^2 , with a freely acting group Γ, and with external string sources implemented via timelike surface operator insertions, is expressed in terms of Ray-Singer torsion of S ^3/Γ and characters of irreducible representations of Γ. We compute it explicitly for the Dicyclic groups. The torsion and characters are generally irrational numbers, but they nicely combine to an integer index. Alternatively, the Witten index can be computed from Chern-Simons theory on S^2 , and Ray-Singer torsion on S^3/Γ  is thus computable from Chern-Simons theory. The matching of the Witten index calculated by these dual approaches reveals new details about the partition function of the (2, 0)-theory with surface operators.

Based on: 2502.18638 a joint work with Andres Franco Valiente and Ori Ganor.