11 problems

Constant-term spectral-action conjecture. The constant term of the spectral action of $\mathcal{D}_A$ on the noncommutative $n$-torus is proportional to the constant term of the sp…

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…

Ward-identity conjecture. The Ward identity, in the sense of van Nieuwenhuizen and Schnitzer (2022), holds in both cases when restricting to the graphs of maximal order of divergen…

Planar maximal-divergence conjecture. Among the $n$-point, $L$-loop graphs, every graph with maximal order in the setting of Theorem … .

Let $g_1$ and $g_2$ be the two diagonal metrics, and let $\widehat{V}(g_1,g_2)$ denote the potential term in the spectral action. Write $\sqrt{g_2^{-1}g_1}$ for the positive square…

Let the Euclidean Robertson–Walker spacetime have scaling factor and its derivatives, and consider the asymptotic expansion of its spectral action. Rationality conjecture. All term…

Let $\mathcal{S}(\mathcal{D}_A,\Lambda,\phi)$ denote the spectral action for a selfadjoint one-form $A$ on the noncommutative torus, and let…

Let $f$ be a piecewise continuous function satisfying the fall-off condition in the source, and let $w$ and $w_\Lambda$ be the functions defined by the formulae referenced as $(w)$…

Consider the spectral action on a noncommutative torus with perturbation … Let $\Theta$ be the deformation matrix, and let the associated Yang--Mills term be…

Let $\mathcal{D}_A$ denote the fluctuated Dirac operator on a noncommutative torus, and let $\mathcal{D}+A$ denote the corresponding operator on the commutative torus. Spectral-act…

Let $\mathcal{D}$ be the Dirac operator on a noncommutative $n$-torus, let $A$ be a selfadjoint one-form, and write $\mathcal{D}_A$ for the corresponding fluctuated Dirac operator.…