75 problems

Let $\Sigma$ be a smooth surface with smooth boundary, endowed with a Riemannian metric. Let $\varkappa$ denote the boundary operator and $D_\Sigma$ the Dirichlet-to-Neumann operat…

Let $\mathfrak{g}^*$ be the homotopy Lie algebra associated with the free massless theory in dimension $d$, and let $G_{M,\mathrm{Betti}}$ be the motivic Galois group in the Betti…

Let $V=\mathbb{R}^d$, let $\Phi$ be the bundle of local fields of a quantum field theory, and let $\Phi_0$ be its fiber at the origin. Let $G_d$ be the group of parallel translatio…

Representation isomorphism conjecture. The corresponding representations of $\mathcal{Z}_q$ and $\widetilde{\mathcal{H}_{GT}}$ on quantum field theories on $S^{4,\theta}$ are isomo…

Let “free” plektons denote the class of free plektonic quantum field theories in $2+1$ dimensions, and let chiral conformal quantum field theories be conformal theories on a one-di…

The transverse symmetry and absence of correlations reduce the area-density problem to a chiral theory on a lightray, which is mapped by a Cayley transform to a chiral theory on th…

Representation-theoretic interpretation conjecture. The quantum field theory of the standard model may be understood purely in terms of the representation theory of the automorphis…

Expected properties of Yang–Mills plus Chern–Simons theory. The following assertions are expected: (1) the Lagrangian determines a family of Wick-rotated field theories; (2) the si…

In the BV formalism, let $I$ be a local interaction for a UV-finite theory, and let $r\to 0$ denote the removal of the regularization. Write $l_n^\hbar$ for the multilinear operati…

Let $X$ be the target of a 3-dimensional $\mathcal{N}=1$ supersymmetric sigma model, and let $X_+$ denote $X$ with a disjoint basepoint. Sigma-model boundary-condition conjecture.…

Let $a^{(+)}(k)$ denote real-space creation or annihilation variables, and let $a^{(+)}(k,\beta)$ and $\tilde{a}^{(+)}(k,\beta)$ denote temperature-dependent primordial variables.…

Let $G(\Lambda,a)$ be the formal series for the two-point function of an asymptotically free quantum field theory, where $\Lambda$ is the kinematical parameter. Suppose its $\beta$…

Let $\mathcal{M}_{\mathrm{lin}}(\mathbb{C}^n,\mathcal{D}'_{\mathrm{reg}}((\mathbb{R}^d)^{\otimes N}))$ denote the space of distribution-valued meromorphic germs with linear poles,…

Let $(M,g)$ be the spacetime under consideration and let $\mathcal{O}inmathcal{K}(M,g)$. Write $\mathrm{QuantLie}$ for the set … Let…

For each loop order $L$, consider the period Feynman integrals of $\phi^4$ theory and sample them with probability inversely proportional to the symmetry factor of their associated…

Let $M$ be a manifold with a tangential structure, and let $F$ be an embedded submanifold that is Poincaré dual to a characteristic class of $M$. A characteristic structure is the…

Primitive beta-function asymptotic conjecture. The leading growth of the primitive beta function satisfies

Haar-wavelet solvability conjecture. For every $\eta\in(\sqrt2-1,1)$, a resolution $\{N_0,N_1,K\}$ can be found such that this finite system admits a solution of the prescribed Haa…

Let $A(N,K)$ be the $(N+1)K\times(N+1)K$ matrix whose entries are the integrals of products of Haar wavelets defined in the paper, and let $\lambda_{\max}(A(N,K))$ denote its maxim…

Let $G$ be a compact Lie group acting on a manifold $X$, let $X{/{\!/}^{\nabla}}G$ denote the quotient stack encoding the action with connection data, and let…

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…

Abelian Higgs correlator theorem. The correlator may be obtained by applying $\mathcal{T}_{\mathrm{cont}}$ to

Källén–Lehmann spectrum conjecture. The free scalar propagator on $M$ has a Källén–Lehmann power spectrum $\rho(m)$ equivalent to

Non-perturbative Noether theorem. If $\cT$ has $X$-symmetry, then there exists a factorizing line bundle $\mc{L}$ on the prefactorization space $X_c$ and a map of prefactorization…

Let $|0\rangle_p$ and $|0\rangle_q$ be the vacuum states in the Hilbert spaces $L^2_p({\cal F})$ and $L^2_q({\cal F})$, respectively, associated with the Sobolev parameters $p$ and…