25 problems

Twistor correspondence conjecture. There is a natural one-to-one correspondence between equivalence classes of these singular self-dual Zollfrei conformal structures and equivalenc…

Closure conjecture. The set $\overline{S}-S$ is a finite subset of $C$, and $\overline{S}$ is a topological manifold.

Let $E$ be a unitary vector bundle with a self-dual connection, let $\widetilde{E}$ be the corresponding holomorphic bundle on the twistor space $M$, and let $n$ be the rank of…

Let $n>1$, fix $z\in\mathbb{C}^n$, and let … where $z=(\xi+w\overline{\xi})/(1-|w|^2)$, so that $X_\varepsilon$ is the image of a twistor-space neighborhood of the ball…

Let $M$ be a Riemann surface with twistor space projection $\pi$, and let $\mathcal{O}$ denote the structure sheaf of the twistor space. Then $R^1\pi_*\mathcal{O}$ is the first hig…

Correspondence conjecture. There exists a correspondence between solutions to the full KP equation and the Moyal deformations of ${\cal Z}$.

Let $k$ be a positive integer, let $a_1,\ldots,a_k$ be parameters, and let $G(\eta,\zeta)$ be the function … Here $\eta$ and $\zeta$ are the variables in the generalized Legendre t…

Let $G(b7,b6)$ be a function used in the generalized Legendre transform construction, and let … These functions arise for hyperkähler metrics whose twistor space projects onto…

Let $X$ be a projective variety, and let $\rho$ be a reductive representation of its fundamental group, assumed reductive after restriction to the fundamental group of the normaliz…

Let $\mathbb{T}$ be the twistor space and consider deformations of its complex structure satisfying the first three conditions of the stated nonlinear graviton theorem: preservatio…

The Penrose–Ward correspondence relates perturbative self-dual Yang–Mills theory to a perturbative holomorphic quantum field theory on twistor space. In particular, perturbative se…

Let $z$ be a complex variable, and define the complex delta function by … Consider delta functions on complex twistor space, constructed using complex integrals and the Čech cohomo…

In Yang–Mills scattering amplitudes, consider the sign factors arising when amplitudes are Fourier transformed from momentum space to real twistor space for split-signature space-t…

Let the deformed twistor space be the complex twistor space described by the Beltrami differential … Q{Lambdanu^2}={(X,Y,Z,eta)in mathbb{CP}^3: XY-Z^2+frac{Lambda nu^2}{2}eta^2=0}…

Nash's decomposition and symplectic-form conjecture. Nash's decomposition coincides with the tangent-space decomposition, and Nash's symplectic forms coincide with the forms…

Let WZW$_4$ plus Mabuchi gravity be the bulk theory on Burns space, and let the large $N$ chiral algebra be the chiral algebra obtained from the compactification…

Let $\widetilde{\mathbb{F}}$ be the Burns-space twistor compactification and let $\overline{\operatorname{SL}}_2(\mathbb{C})$ be the alternative compactification. Consider holograp…

Gaiotto–Moore–Neitzke's variation conjecture. A variation of the Gaiotto–Moore–Neitzke construction should work on $\mathcal{M}$ with those necessary adjustments.

Gaiotto–Moore–Neitzke's twistor reconstruction conjecture. Then $\mathcal{Z}:=\mathcal{M}\times\mathbb{C}\mathbb{P}^1$ has all the structure necessary for the twistor construction,…

Let $l$ be the loop order and let $q$ be the number of gluons of negative helicity in a scattering amplitude. After the half-Fourier transform from momentum space to twistor space,…

Higher singularity conjecture for sheaf lines. The order of singularity of a sheaf line is higher than that of other normal jumping lines.

The six-dimensional spin-two field strength $G_{ABCD}$ is chiral and has five on-shell degrees of freedom, in contrast with the conventional graviton. Superconformal (4,0) theory c…

Mason's conjecture. When weighted by the exponential of this new action, $\big\langle\mathrm{W}[C]\big\rangle$ yields the complete planar S-matrix of $\mathcal{N}=4$ super YangMill…

Witten's conjecture. In general, $\ell$-loop $\mathrm{N}^k\mathrm{MHV}$ superamplitudes localise on rational curves in supertwistor space which have

LeBrun–Mason type correspondence conjecture. There is a natural one-to-one correspondence, at least in a neighborhood of the standard objects, between equivalence classes of space-…