303 problems

Maldacena's AdS/CFT correspondence. String theory on an asymptotically AdS spacetime should be equivalent to a conformally invariant quantum field theory on its boundary.

Let $W$ be a D$p$-brane world-volume embedded in space-time $X$ by $\iota:W\hookrightarrow X$, and let $E\rightarrow W$ be the rank-$q$ Chan–Paton bundle. If $W$ is spin$^c$ with a…

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…

In a quantum-gravitational theory with a moduli space of vacua, consider an asymptotic boundary of the moduli space. Emergent String Conjecture. A weakly coupled string should emer…

All-loop BPS symmetry conjecture. The algebra $\mathfrak{g}$ is a symmetry of BPS amplitudes at all loop orders.

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…

In the infinite momentum frame, let $N$ point-like D0-branes be described by quantum mechanics, with their dynamics governed by a supersymmetric matrix model. BFSS M-theory conject…

Mirror symmetry concerns pairs of Calabi–Yau compactifications related by exchanging the geometric data of the two theories. In the flux setting, one considers compactifications of…

A Calabi–Yau manifold is a compactification space for the extra six dimensions of the heterotic string, while an $\mathcal{N}{=}2$ superconformal field theory (SCFT) describes the…

A non-supersymmetric anti-de Sitter solution is a solution with negative cosmological constant that does not preserve supersymmetry. Ooguri–Vafa conjecture. Any non-supersymmetric…

Let a consistent low-energy effective theory coupled to gravity have a moduli space of theories, and consider an infinite-distance limit in that moduli space. Distance Conjecture.…

String theory constructions have had difficulty producing a de Sitter background compatible with a complete higher-dimensional theory. De Sitter conjecture. Such a background canno…

The intermediate random-matrix ensemble described in the paper arises from $U(N)$ Chern–Simons theory on $S^3$, an interacting topological system exhibiting ergodic-to-nonergodic t…

Let a homogeneous Yang–Baxter deformation be a deformation defined by a skew-symmetric classical $r$-matrix solving the homogeneous classical Yang–Baxter equation, and let a non-Ab…

Type IIB supergravity has an $SL(2,\mathbb R)$ duality group, with the axio-dilaton transforming under this symmetry. Type IIB S-duality conjecture. The subgroup $SL(2,\mathbb Z)$…

The IKKT matrix model is a dimensionally reduced ten-dimensional super Yang–Mills theory whose degrees of freedom are described by ten Lie-algebra-valued matrices and their sixteen…

In closed string theory, Ricci flow arises as a first-order world-sheet renormalization-group flow. Off-shell processes in string field theory, such as tachyon condensation, are co…

Let $Z_{\mathrm{ghost}}^{(2)}(\Omega)$ denote the genus-two partition function of the fermionic central-charge-$-26$ ghost conformal field theory, and let $q_1,q_2$ and $\epsilon$…

Dixon–Harvey–Vafa–Witten conjecture. The Euler characteristic of $Y$ should satisfy

Let $R={\bf C}[K]$ be the semigroup ring of lattice points of the graded cone $K$, and let the explicitly constructed regular sequences in $R$ be given. Quotient conjecture. The qu…

Let $t$ denote the parameter in the renormalization-group flow equation for the nonlinear sigma model describing quantum strings in a background spacetime, and let a fixed point be…

Let $N$ denote the rank parameter of a gauge theory, and consider the large-$N$ limit. ’t Hooft's conjecture. Large-$N$ gauge theories are dual to closed string theories. The sourc…

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 a three-dimensional Calabi–Yau orbifold and let $\widetilde{X}\to X$ be a crepant resolution. Orbifold K-theory records the parity-graded K-theoretic information associa…