12 problems

Let $Z_{BH}$ denote the black hole partition function and let $Z_{\text{top}}$ denote the topological string partition function. OSV conjecture. The black hole partition function e…

Strong Height conjecture. There exist a finite positive constant $\kappa$, possibly depending on the family, and a choice of model for each $X_{\gamma_n}$ such that

Weak Strominger–Vafa conjecture. If $\{\gamma_n\}$ is a big sequence, then

Strong Strominger–Vafa conjecture. If $\{\gamma_n\}$ is a big sequence, then $S_{\rm micro}(\gamma_n)$ has an asymptotic expansion in $z_n$, more precisely

Localization entropy area-law conjecture. The restriction of the vacuum state to the local algebra including the collar may have finite entropy for every sufficiently small…

Consider Chern--Simons theory on four-fibered Seifert manifolds and the associated boundary-crossing method for resurgent continuation across the Chern--Simons natural boundary. Bo…

Moonshine-module heterotic theory conjecture. Such a theory can be found by making this replacement.

Handle-degeneration conjecture. In the classical limit, the handles of $\Sigma$ should progressively become thinner and thinner until their volume degenerates.

Long-string entropy conjecture. The degeneracy of the states of the long string could explain the black-hole entropy, and the black hole itself could be treated as the long string…

The entropy step constant is defined by … Here $\Delta a$ is the characteristic width of the entropy steps, while the subscripts DL, GM, and ENP denote the different loop-quantum-g…

Let $(M,g_{ab})$ be a smooth classical spacetime and let $p$ be a point in it. Consider the future null cone of $p$, and let $B$ be any 2-sphere cross-section of the null cone such…

In loop quantum gravity, the black-hole entropy spectrum exhibits a quantization phenomenon, characterized by a preferred spacing in the entropy or area spectrum. Macroscopic-black…