435 problems

Irreducibility conjecture. The family of representations $\mathcal{H}_{\bar{\rho}}^+$ is irreducible.

Let $G$ be a connected graph, let $X_G$ be its graph hypersurface, and write $[X_G]_q=|X_G(\mathbb F_q)|$ for its point-counting function over finite fields. Inspired by the appear…

Let $G=\{G_d,s_d,\rho_d\}_{d\in\mathbb Z_{\ge 0}}$ be a system of compact Lie groups with structure maps $s_d\colon G_d\longrightarrow G_{d+1}$ and representations…

QED is quantum electrodynamics and QCD is quantum chromodynamics. Feynman's quantum-simulation conjecture. Computations in high-energy physics, especially computations in QED and Q…

Infrared-finiteness conjecture. With the right choice of the numerical part of the current, there are no infrared divergences in the formalism of L-functionals if, in perturbation…

In perturbative $phi^4$ theory, consider the beta function renormalized in the minimal-subtraction (MS) scheme, and call a Feynman graph primitive if it has no subdivergences. Prim…

Beem–Rastelli conjecture. The Higgs branch of the 4d SCFT should coincide with the associated variety of the corresponding 2d CFT.

Let $\Omega$ be the region occupied by the quantized field, with boundary $\partial\Omega$, and let $p_i^{\mathrm{ren}}({\bf x})$ be the renormalized pressure obtained by analytic…

String theory is described as non-localizable because there is a fundamental length $\ell>0$ below which events cannot be distinguished. In this setting, the usual local commutativ…

Mixed-Tate motives are motives belonging to the tannakian subcategory generated by Tate motives, and a period is a number arising from the comparison between algebraic de Rham and…

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…

Consider the Sine–Gordon model with action … Here $\beta>0$ is the coupling constant, $g$ is the interaction cutoff, and the massless model has solitons and anti-solitons. The mass…

The Bose polaron considered by Lampart is defined with an ultraviolet cutoff, and the method developed in this paper is an ultraviolet renormalisation procedure for constructing a…

The full quantum differential is the BV differential … Let $\mathcal{V}$ denote the cohomology of the underlying free and classical theory, and let $\mathbf{Q}$ be a differential o…

Seiberg's deformation conjecture. Any quantum field theories with the same symmetry $G$ and the same anomaly ${\mathbf{Z}}_{d+1}$ can be deformed to each other by adding degrees of…

Panzer–Schnetz coaction conjecture. The Galois coaction closes on $\phi^4$-periods:

The Unruh state is a distinguished quantum state for a massless field on a black-hole spacetime, constructed here in the slowly rotating Kerr setting and shown in the source to hav…

The $p$-adic setting uses a non-Archimedean spacetime, meaning that spacetime is modeled over a field with a non-Archimedean absolute value. Volovich's conjecture. Spacetime has a…

Bell-polynomial identity. For any $l,n_0,\dots,n_p\in\mathbb{N}$, the Bell polynomials satisfy the identity

A $CPT$-symmetric field theory is a field theory invariant under the combined action of charge conjugation, parity, and time reversal. A field theory is non-Hermitian when its Hami…

Let $E$ be the regularized vacuum energy in dimension $3$, let $\Delta=(\kappa_1-\kappa_2)^2$, and let the ultraviolet regularization parameter tend to $0$. Compensating boundary t…

In a quantum field theory satisfying the Weak Reichenbach's Common Cause Principle, let $A$ and $B$ be correlated events associated with spacelike separated regions. A common cause…

Let $g_{2n}$ be the representation-dependent factors in the coefficients $w_{2n}$ of the Wilson-loop expansion, and let $c_2$ and $c_v$ denote the quadratic Casimir factors appeari…

Conjecture on generation of reordering identities. All identities based on the reordering of summation ranges are generated by this reflection identity. The conjecture concerns the…

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…