23 problems

Let ${\mathcal P}_+$ denote the set of nonempty partitions, let $\mu^+$, $\mu^-$, $\nu^+$, and $\nu^-$ be partitions, and let $G_{\mu^+,\mu^-}(\tau)$ be the specialization defined…

Let ${\mathcal P}$ be the set of partitions, let $\mu^+$ and $\mu^-$ be partitions, and let $G_{\mu^+,\mu^-}(x,y)$, $p^+_{\mu^+}$, and $p^-_{\mu^-}$ denote the corresponding genera…

Let $X$ be an $r$-dimensional normal complex variety having at most Gorenstein canonical singularities. Its string-theoretic index is the least positive integer $l$ such that…

Let type IIA string theory be compactified on $T^d$ with $d\leq 4$, let $\phi$ be the T-duality-invariant dilaton, let $H_{RR}$ denote the Ramond three-form field strengths, and le…

Let $I_d^g$ be the integral of the $(d,d)$ lattice partition function over the fundamental domain of the moduli space of genus-$g$ Riemann surfaces, and let…

Let type II string theory be compactified on $T^d$, equivalently M-theory on $T^{d+1}$, and let $E_{d+1(d+1)}(\mathbb{Z})$ be the U-duality group. Denote by…

Let $\mathcal{Z}$ be the string partition function, let $x$ be the string coupling parameter, and let $F_0^{(0)}$ and $F_1^{(0)}$ be the classical genus-zero and genus-one potentia…

Leading-pole cancellation conjecture. The choice

Let $\mathfrak Y$ be a compactification with higher supersymmetry, let $\gamma=(p^0,p^A,q_A,q_0)$ be an electromagnetic charge vector, and let … After restricting to the sublattice…

A GLSM is a gauged linear sigma model, and worldsheet $(0,1)$-supersymmetry is supersymmetry with this chirality structure. De Sitter realization conjecture. GLSMs with worldsheet…

Charged-multiplet conjecture. The charged multiplets $H_{ch}$ in the massless spectrum satisfy

Scale-separation conjecture. Classical de Sitter solutions cannot have at the same time a large internal volume, a small string coupling, a bounded number of orientifolds and quant…

Intersecting-source instability conjecture. Classical de Sitter solutions with intersecting sources are unstable.

Parallel-source conjecture. There is no classical de Sitter solution with parallel sources.

Let $\mathcal{C}$ be the cone in the source, let $A_f$ denote the corresponding finite or smooth-part algebra, and let $H_{\mathfrak{a}}^{i+\frac{\infty}{2}}(A_f)$ be the semi-infi…

BCOV theory is a closed-string field theory for the topological $B$-model, formulated here on complex affine space. Type IIB supergravity is the ten-dimensional supergravity theory…

In the $(p,q)$-system, let $\mathfrak g$ be defined by $2\mathfrak g=(p-1)(q-1)$, and let $\{\theta_a\}_{a=1}^{2\mathfrak g}$ denote the D-instanton and ghost D-instanton fugacitie…

Let $\mathcal A$ be an associative algebra equipped with a differential … For a theory with a single D-brane, the deformation data are encoded by $(\mathcal A,Q)$, and their equiva…

Denef–Moore conjecture. (i) The invariant $\operatorname{DT}_H(0,mH,-\beta,-n)$ vanishes unless

Let $G$ be a finite group acting on $\mathbb{C}^3$, and let $X$ be its three-dimensional $G$-Hilbert scheme, a crepant resolution when the construction applies. The $(0,2)$)-deform…

Let $\mathcal{C}$ be the configuration space of string vacua, and let physically distinct vacua be points of this space. Acharya–Douglas minimal-distance conjecture. There exists a…

Let ${\bf Spaces}$ be the category of spaces, let ${\rm \ker}\,\mathbf{Q}$ be the proposed $L_\infty$ category, and let $HH({\bf Spaces})$ denote the Hochschild cohomology of…

Let ${\mathfrak{l}}$ denote the composition structure on the category ${\rm \ker}\,\mathbf{Q}$, where the propagators of open string fields are defined from the Poisson-type sigma m…