An emergent higher-form symmetry from type IIB superstring theory

We investigate a higher-form symmetry in type IIB superstring theory, which possesses an SL(2,Z) symmetry. From the point of view of the low-energy effective field theory, the SL(2,Z) symmetry is treated as a gauge symmetry. Hence, an $8$-form global symmetry Z₁₂[8] emerges as a quantum symmetry. In this paper, we present an explicit construction of the topological operator associated with the Z₁₂[8] symmetry. In this construction, the discriminant $Δ(τ)$ plays a central role. As a result, it becomes manifest that Z₁₂[8] is the solitonic symmetry of $7$-branes. Furthermore, taking into account the extensions of the duality group, we also discuss what global symmetries emerge when considering not SL(2,Z) but Mp(2,Z), GL(2,Z), and Pin⁺( GL(2,Z))= GL⁺(2,Z).