7-branes and ${\Gamma }_0(2)$ Duality in Type 0B String Theory

Abstract

We investigate 7-branes in type 0B string theory, motivated by the recent proposal of Baykara, Dudas, and Vafa, which connects type 0B string theory with M-theory. On the $Q$-symmetric branch, the self-duality group of type 0B string theory is ${\Gamma }_0(2)$, whose Abelianization is $\mathbb{Z}\times {\mathbb{Z}}_4$. This implies the existence of two independent 7-brane charges. We construct explicit charge operators in terms of modular forms and identify the corresponding charged objects in gravity solutions. One is the ordinary D7-brane, while the other is a 7-brane carrying a nontrivial ${\mathbb{Z}}_4$ charge. We further construct a compact background consisting of eight such ${\mathbb{Z}}_4$ 7-branes using a restricted Weierstrass model. Remarkably, in this background the axio-dilaton is fixed to the constant value $\tau =(1+\mathsf{i})/2$, which coincides with the unstable de Sitter critical point proposed in the M-theory description of type 0B string theory. We also analyze fluctuations in the $Q$-odd sector and find that, although the corresponding equations of motion are globally well-defined in this background, the closed string tachyon remains unstable. Our results provide a concrete realization of new 7-branes in type 0B string theory and clarify their relation to its strong-coupling structure.

26 pages