251 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 the moduli space of an effective theory be equipped with its field-space metric, and consider a point at infinite geodesic distance. Swampland Distance Conjecture. For a viable…

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…

Quantum foam conjecture. The statistical model of random plane partitions is nothing but quantum Kähler gravity.

Bousso's covariant entropy conjecture. Every such light-sheet obeys this entropy bound. The conjecture generalizes a Bekenstein-like entropy formula to a wider class of spacetime r…

Swampland Cobordism Conjecture. The bordism groups of quantum gravity are trivial:

The two-dimensional Jackiw–Teitelboim (JT) gravity is a toy model of quantum gravity and holography, and the $(2,p)$ minimal string is the corresponding minimal-string theory with…

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.…

The asymptotic-safety program seeks a non-trivial ultraviolet fixed point of the renormalization-group flow that can provide a quantum-field-theoretic ultraviolet completion of gra…

Let $A$ be the area of a black hole's event horizon, let $l_P$ be the Planck length, and let $\kappa$ be a dimensionless constant of order unity. Bekenstein's event-horizon area qu…

Born's reciprocity principle. The basic underlying physical space should be the eight-dimensional phase space with coordinates $\\{x_\mu,p_\mu\\}$, and the Poincaré line element sh…

Let the on-mass-shell momentum-space scattering amplitudes of gravity and gluon scattering amplitudes in Yang–Mills theory be considered in perturbation theory. Gravity double-copy…

The paper considers quantum gravity, general relativity, quantum theory, and a proposed causality superselection rule expressed through the nondemolition principle, according to wh…

Gravitational manifestation conjecture. In some yet-to-be-found sense, the gravitational field is a classical manifestation of the noncommutative micro-structure of space-time.

The proposed quantum theory $X$ is defined purely algebraically, without background geometry, and has classical limit $3+1$ general relativity coupled to certain matter fields. The…

A theory with a quadratic Hamiltonian constraint has a two-sheet structure, and the clock reversal transformation is the symmetry associated with passage from one sheet to the othe…

For quantized gravitational fluctuations around a symmetric background spacetime, quadratic constraints suppress transitions to configurations of lower symmetry. Enhancement–suppre…

String configurations are extended objects in string theory, and at distances below the Planck length $l_P$ the conventional notion of spacetime geometry may cease to be adequate.…

David–Distler–Kawai conjecture. The Jacobian arising from the use of this translation-invariant measure is given by the exponential of the Liouville action with modified coefficien…

Let $\gamma$ be a loop and let $\operatorname{Jones}_\Lambda(\gamma)$ denote the Jones Polynomial appearing in the expansion of the Kauffman Bracket with cosmological constant…

Let ${\bf H}$ be the space of solutions of the Hamiltonian constraint with a basis given by isotopy classes of tangles, and let ${\cal T}$ be the algebra generated by the annihilat…

Consider superstring theory with ground states, including the ground state leading to ten-dimensional space-time, and consider compactification on Calabi–Yau threefolds as a possib…

In superstring theory, consider compactification on a Calabi–Yau 3-fold, and let the translation group contain a four-dimensional subgroup corresponding to the uncompactified direc…

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…

Let the fermionic matrix integral be defined by the matrix model in the source, with matrix size $N$, and consider its genus expansion in the large $N$ limit. Borel summability con…