69 problems

The Skyrme–Faddeev model is a theory in $(3+1)$-dimensional Minkowski space-time whose field is a unit vector ${\vec n}$ taking values on $S^2$, with a quadratic kinetic term and a…

The physical configuration space of a gauge theory may be compact in certain directions, as indicated by the possibility that the averaging integral has infinitely many stationary…

Yang–Mills mass gap conjecture. For any compact simple Lie group $G$ there exists a nontrivial Yang–Mills theory on the Minkowskian $\mathbf{R}^{1,3}$ whose quantization satisfies…

The Yang–Mills functional is defined on the infinite-dimensional space of connections over a compact Riemann surface, with the gauge group acting on this space. An equivariantly pe…

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…

Let $M$ be an $n$-dimensional Riemannian manifold and let $\{(A_i,S_i)\}$ be a sequence of stationary admissible Yang–Mills connections on a bundle $E$, with bounded Yang–Mills ene…

Proportionality conjecture. This definition should give a Yang–Mills action proportional to the logarithmically divergent part of the fermion effective action for other four-dimens…

Let $k>3/2$. In temporal gauge $A_0=0$, let … be the Banach space of Cauchy data $(A^{\operatorname{Cau}},\dot A^{\operatorname{Cau}},\Psi^{\operatorname{Cau}})$, and let…

String interpretation conjecture. The chiral intersecting Wilson loop amplitudes are obtained by imposing the boundary condition that $f:\partial\Sigma_W\to\amalg\Gamma$ lies in th…

The perturbative construction associates to a curve configuration a sequence of area-preserving-diffeomorphism invariants. Projection conjecture. This sequence of invariants should…

Let $G_N$ be an increasing sequence of groups, and specialize to $G_N=SU(N)$. For sequences $U_{Nj}\to \sigma_j$ with $U_{Nj}\in SU(N)$ and limiting eigenvalue probability measures…

The paper considers Yang–Mills gauge potentials whose asymptotic expansion is … with coefficients depending only on $\tau$ and $a$, and imposes the conditions obtained from the Yan…

In Einstein–Yang–Mills theory, consider black hole solutions with non-trivial Yang–Mills fields and horizon charges encoding the relevant horizon data. Corichi–Nucamendi–Sudarsky c…

Let the strict $\mathrm{BV}^{\square}$ algebra identified in the paper be given, and let the full $\mathrm{BV}_{\infty}^{\square}$ algebra of Yang–Mills theory be given. A suitable…

Conditional asymptotic stability conjecture. The orbit $\mathcal O_H$ is conditionally asymptotically stable in the energy space: roughly, for initial data of the form…

Wilson-loop gauge/string duality conjecture. The gauge/string duality should extend beyond the partition function and hold for Wilson loop expectations.

Higher-genus gauge/string duality conjecture. The torus gauge/string duality should admit a generalization to every genus $g\geqslant 2$, involving not only the expansion of the he…

Yang–Mills/string duality conjecture. The observables of $\mathrm{YM}_2$ should be related to string theory.

Let $\Sigma_g$ be a compact surface of genus $g\geq 0$, with structure group ${\mathrm{SU}}(N)$. Consider its Yang–Mills partition function and Wilson loop expectations. Gross–Tayl…

Let $A(t)$ be a flow of connections on a vector bundle $E$ over a manifold $M$, and let $U(t)=U^{A(t)}$ denote the corresponding flow of parallel transports, regarded as sections o…

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…

In four dimensions, consider non-Abelian Yang–Mills theories with inverse coupling constant $\beta$, a parameter governing the amount of order or disorder in the system. Area-law c…

Weak-coupling Yang–Mills mass gap conjecture. For any bare coupling constant $g\in[0,g_0[$, the spectrum of $H^g$ contains $0$ as a simple eigenvalue for the vacuum eigenstate and…

Four-dimensional Yang–Mills measure-properties conjecture. The classic Hamiltonian system can be quantized so that $\mu^g$ exists, $S^g$ satisfies the Osterwalder–Schrader axioms (…

Let $G$ be the gauge group and let the nontrivial Yang–Mills theory on Minkowskian spacetime $\mathbf{R}^{1,3}$ be the theory whose existence and quantization are asserted by the Y…