Emergent higher-form symmetry from type IIB superstring theory

Abstract

We investigate a higher-form symmetry in type IIB superstring theory, which possesses an $\mathrm{SL}(2,\mathbb{Z})$ symmetry. From the point of view of the low-energy effective field theory, the $\mathrm{SL}(2,\mathbb{Z})$ symmetry is treated as a gauge symmetry. Hence, an $8$-form global symmetry ${\mathbb{Z}}_{12}^{[8]}$ emerges as a quantum symmetry. In this paper, we present an explicit construction of the topological operator associated with the ${\mathbb{Z}}_{12}^{[8]}$ symmetry. In this construction, the discriminant $\hat{I}”(\ddot{I}„)$ plays a central role. As a result, it becomes manifest that ${\mathbb{Z}}_{12}^{[8]}$ 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 $\mathrm{SL}(2,\mathbb{Z})$ but $\mathrm{Mp}(2,\mathbb{Z})$, $\mathrm{GL}(2,\mathbb{Z})$, and ${\mathrm{Pin}}^{+}(\mathrm{GL}(2,\mathbb{Z}))={\mathrm{GL}}^{+}(2,\mathbb{Z})$.

20 pages