93 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…

In the case where all fluxes vanish, a twisted background is a Calabi–Yau metric together with a covariantly constant pure spinor. The associated BCOV (or Kodaira–Spencer) theory i…

Conjecture on three-quarters supersymmetry. There exist backgrounds with $\nu=\tfrac34$ which are not locally homogeneous.

Let $\mathbb{V}$ be a finite-dimensional real vector space with a euclidean or lorentzian inner product, let $p\geq 2$, and let $F\in\Lambda^p\mathbb{V}^*$. For…

U-duality conjecture. The discrete subgroup $\mathcal{E}_{d(d)}(\mathbb{Z})$ lifts to a symmetry of the full string theory.

Dimensional reduction of ${\rm D}=11$ supergravity on tori gives a sequence of hidden symmetry groups $\mathrm{E}_n$, with reductions to lower dimensions requiring dualization of h…

Let $\mathcal{M}$ be a manifold with boundary $\partial\mathcal{M}$, and let $B_m$ denote the supergravity field appearing in the boundary action. The action may contain terms prop…

The type-II compactification is described by pure spinors $\Phi^+$ and $\Phi^-$ on the internal six-manifold, and the three prepotentials $\mathcal{P}^x$ are given, for type IIA, b…

For $d>2$, let $G(\mathrm{spacelike})$, $G(\mathrm{timelike})$, and $G(\mathrm{null})$ denote the groups obtained respectively from spacelike, timelike, and null dimensional reduct…

Let the $D=11$ supergravity fields be the graviton $g_{MN}$, gravitino $\Psi_M$, and three-form gauge field $A_{MNP}$. The equations of motion are considered without compactificati…

Matroid bundles are combinatorial analogues of vector bundles, with oriented matroids playing the role of tangent spaces or, more generally, vector spaces. The authors introduce th…

Courant contact model conjecture. The Courant contact model coincides with the twist of supergravity for the chosen twisted background. The model is equipped with a BV symplectic f…

Let a twisted background be a supersymmetric background of ten-dimensional $\mathscr N=1$ supergravity, and let its Courant contact model be the BV theory obtained from the associa…

Consider de Sitter solutions in theories with a specified number of supercharges. Four-supercharge bound conjecture. De Sitter solutions do not exist in theories with more than $4$…

Consider de Sitter solutions of string theory or supergravity containing orientifold-plane or D-brane sources, denoted $O_p/D_p$. Three-intersecting-sets conjecture. De Sitter solu…

Let $\mathcal E_{\mathrm{twist}}$ be the Courant algebroid associated to the twist, and let the extended BPS complex be the complex for $G=U(5)\times SO(10+k)$ associated to the co…

Let $\mathcal E_{\mathrm{twist}}$ be the Courant algebroid over the Dolbeault complex associated to a twist datum. The Costello–Li twist of type I supergravity is the perturbative…

Let $E$ be the Courant algebroid underlying a twisted supergravity background, and let $L\subset E\otimes\mathbb C$ be the involutive isotropic subbundle determined by that backgro…

Let $\mathcal{M}$ be a manifold on which supergravity dynamics is studied, and consider the hyperbolic Kac–Moody symmetries appearing in cosmological billiards. Hidden-current symm…

Let $\mathcal{M}$ be an internal manifold with isometries, let $\mathfrak{g}(\mathcal{M})$ be its generalized Kac–Moody current algebra, and let flux backgrounds define the reduced…

Let $\mathcal{M}$ be a manifold and let a consistent truncation admit a global orthonormal frame, such as a generalized parallelisation. Let $\mathfrak{g}(\mathcal{M})$ denote the…

The paper considers 11-dimensional supergravity and its conjectured ultraviolet completion, referred to as M-theory. M-theory conjecture. Some completion of 11-dimensional supergra…

Let $N^X_{\mathfrak{g},0}(\lambda,\epsilon)$ denote the constant-map contributions to the topological-string expansion on $X$, with $N^X_{1,0}(\lambda,\epsilon)$ the genus-one cont…

The theory under consideration is the B-model topological string theory, or BCOV theory, with target $SL(2,\mathbb{C})$, holographically related to the protected chiral algebra sub…

Supersymmetry conjecture. The solution presented in the paper is supersymmetric when