21 problems

The constructions under discussion arise from toric tops and their associated elliptically fibered Calabi–Yau geometries. In particular, K3 compactifications and the corresponding…

Let $F_g(t)$ be the generating function of genus-$g$ open topological-string amplitudes with boundary weights $t$. Open/closed string duality. There is a family $\tilde M(t)$ of Ca…

The new type IIB vacua under discussion are described by elliptically fibered Calabi–Yau manifolds, with the dilaton varying over an elliptic curve. On the heterotic side, consider…

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…

Let A denote the $N=2$ heterotic string compactified on $K_3 \times T_2$, and let B denote the $N=2$ type II superstring compactified on a Calabi–Yau threefold. Their moduli spaces…

Let $B'$ be a $\mathbf{P}^1$-bundle over $B$, with $B'=\mathbf{P}({\mathcal O}\oplus {\mathcal T})$, and let $X\to B'\to B$ be the corresponding elliptically fibered fourfold. Let…

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…

The objects are string theory on the near-horizon geometry of $NS5$-branes and the decoupled theory on their world-volume. NS5-brane duality conjecture. String theory on the near-h…

Gopakumar–Vafa conjecture. The free energy $F$ can be expressed as

Fiber-wise duality conjecture. This fiber-wise duality should work remarkably well when there is some residual supersymmetry and an underlying adiabaticity.

Transverse-distance conjecture. The transverse distance between the D3-brane probe and the $E_n$ 7-branes is proportional to $\operatorname{vol}(V_2)$ in the local Calabi–Yau three…

Let $X$ be a CalabiYau $5$-fold. The type I topological string on $X$ is the unoriented topological $B$-model with its open-string sector, whose gauge theory has structure group…

The type I topological $B$-model has fields given by the $/2$-fixed points of KodairaSpencer theory on a CalabiYau $5$-fold, coupled to an ${\rm SO}(32)$ holomorphic ChernSimons th…

M-theory–heterotic duality conjecture. One could anticipate a duality

The setup involves configurations with two elliptic parameters, $\rho$ and $\tau$, associated with the compactification directions of the little string theories. Bhardwaj's T-duali…

Consider the $SO(32)$ heterotic string compactified on a two-torus with constant abelian gauge flux, which is S-dual to the Type I string with the same gauge flux. T-duality in one…

ABJM type IIA string duality conjecture. ABJM theory has been conjectured to be dual to type IIA superstring theory on $\operatorname{AdS}_4\times {\mathbb C}{\mathbb P}^3$.

Let $\mathrm{U}$ denote the continuous supergravity duality group, and let $\mathrm{U}(\mathbb{Z})$ be its subgroup obtained by restricting the group parameters to integers. String…

Let $N_1=N_2=N$, and consider the ${\cal N}=3$ flavored theory obtained from ABJM theory by adding $N_f=N_f^{(1)}+N_f^{(2)}$ fundamental matter multiplets. The undeformed theory ha…

Let $K3$ be a K3 surface with an involution $\sigma$, let $E$ be an elliptic curve identified with a two-torus, and consider the quotient … Suppose the singular set of the action…