66 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 $A$ be a subregion of the conformal boundary of an Anti-de Sitter spacetime, let $\text{CFT}$ denote the associated conformal field theory, and let $\Sigma$ be the minimal surf…

Let $SU(N)_k$ Chern–Simons theory have a bulk fusion category of anyonic topological sectors, and let the boundary CFT have local operators and topological defect lines. Bulk–bound…

Higher-spin theories on twistor space are built from vector bundles and their associated curvature forms; their one-loop anomaly is governed by the index…

Let $U(N)_{k}\times U(N+M)_{-k}$ denote the ABJ theory, with $N$ finite and with $M$ and $k$ taken large. ABJ/Vasiliev duality conjecture. In this limit, the theory is dual to the…

Let $k$ be the orbifold order, let $S^{7}/\mathbb{Z}_{k}$ denote the quotient of the seven-sphere by the action $y^{A}\mapsto e^{2\pi i/k}y^{A}$ on its four complex coordinates, an…

Let AdS space be an anti-de Sitter space with conformal boundary, and let a quantum field theory (QFT) on AdS space and a conformal quantum field theory (CFT) on its boundary be gi…

Let $N$ be the number of colors and let $g$ be the YangMills coupling, with 't Hooft coupling $\theta=Ng^2$. Consider type IIB string theory on five-dimensional asymptotically Anti…

M2-brane duality conjecture. The dual theory is the $2+1$-dimensional $N=8$ superconformal field theory living on the M2 brane.

Let $X^5$ be a generic Sasaki–Einstein manifold, and consider the states obtained from D3-branes wrapping an $S^3$ inside $AdS_5$ and moving along a trajectory in $X^5$. BPS-geodes…

Let $X$ be an isolated conical Calabi–Yau $3$-fold singularity with link $L$, and consider the four-dimensional $\mathcal{N}=1$ superconformal field theory obtained in the low-ener…

Let maximally supersymmetric ${N}=4$ Yang–Mills theory be taken in the planar limit, meaning the large-$N_c$ limit with the 't Hooft coupling held fixed. At strong coupling, consid…

A Sasaki–Einstein five-manifold $X_5$ is an Einstein manifold whose metric cone is Ricci-flat and Kähler, hence a Calabi–Yau threefold. The product $AdS_5\times X_5$, equipped with…

Let a contour in the boundary of $AdS_5$, close to a circular contour, satisfy the two necessary conditions described in the paper: it is contact, and the second one-form defined o…

Let a holographic boundary state be given at a specified boundary time, and let its computational complexity be the minimal computational cost of preparing that state. Let the dual…

AdS/CFT complexity conjecture. Certain quantum states arising in the AdS/CFT theory have high state complexity, and the growth of this complexity is related to the growth of gravit…

In AdS/CFT, let $\ell$ denote the bulk wormhole length and $t$ the boundary time, with $S_0$ the extremal entropy. Complexity-based saturation conjecture. The bulk volume, and henc…

Let the bulk contain an internal compact manifold $\mathcal{M}$ with a specified isometry algebra, and let $\mathfrak{g}(\mathcal{M})$ be the associated generalized Kac–Moody curre…

Consider the Gibbs state $\rho_{\beta}=\frac{1}{\operatorname{Tr}e^{-\beta H}}e^{-\beta H}$ and its thermofield-double purification $\omega_{TFD}$ in the GNS representation of the…

Consider the large-$N$ algebra $\mathcal{A}_{\beta}$ generated by single-trace operators in $\mathcal{N}=4$ SYM at temperature $1/\beta$. Let…

Let $\mathcal{N}=4$ supersymmetric Yang–Mills theory have gauge group $SU(N)$ on $\mathbb{R}\times S^{3}$, and consider its large-$N$ limit. Let $Ads_{5}\times S_{5}$ denote the c…

AdS/CFT conjecture. AdS/CFT should hold in general settings, although no rigorous proof is currently known.

Let an asymptotically AdS geometry be a gravitational background, and consider string segments propagating in it together with excited states of the dual conformal field theory. Lo…

Let the boundary CFT associated with $SU(N)_k$ Chern–Simons theory have an operator algebra of boundary topological defects. A modular tensor category is a braided fusion category…

AdS/CFT correspondence. Type IIB string theory on $\mathrm{AdS}_5\times\mathrm{SE}^5$ is equivalent to a four-dimensional $N=1$ superconformal quiver gauge theory. The statement is…