13 problems

Consider the type-II orientifold string theories listed in the second column of table 1, together with the more general conventional orbifold theories appearing in that column. Typ…

The $K3\times S^1$ compactification of type-IIB superstring theory is a candidate dual theory, and let $T^5/{\mathbb Z}_2$ denote the corresponding orbifold of M-theory. K3–M-theor…

Conjecture. The quantity

Consider a noncompact Calabi–Yau threefold whose orientifolded geometry undergoes a local geometric transition: two contracted copies of $\mathbb{P}^1$ and one contracted copy of…

Type I twist conjecture. The twist of the type I string is the type I topological string, which is an orientifold of the familiar topological $B$ model.

Let $\overline{D}$ be a vertical divisor in the elliptically fibered geometry, let $\chi_n(\overline{D})$ denote its naive Euler characteristic, and let $n_{O3}(\widehat{D})$ be th…

Type D one-loop Hodge equality conjecture. For $e,k\geq 1$,

Orientifold primitive-cohomology conjecture. The surjection

Orientifold CoHA structure conjecture. The CoHA action map

Orientifold Hodge equality conjecture. The canonical surjection

Orientifold CoHA freeness conjecture. If $\mathcal{H}_Q$ is supercommutative, then the CoHA action map

BPS-state counting conjecture. The unoriented topological string can be rewritten by counting single-particle BPS states.

Orientifold realization conjecture. The refined topological string at