We study the $SU(\ensuremath{\infty})$ lattice Yang-Mills theory at dimensions $D=2$, 3, 4 via numerical bootstrap method. It combines loop equations, with a cutoff ${L}_{\mathrm{max}}$ on maximal length of loops, and positivity conditions certain matrices Wilson averages. Our algorithm is inspired by pioneering paper P. D. Anderson M. Kruczenski [Nucl. Phys. B921, 702 (2017)] but it significan...

We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us to study the low-energy dynamics by explicitly extracting the topological degrees of freedom such as magnetic monopoles and vortices to clarify the mechanism ...

In this first section we attempt to give a brief overview of mathematical work related to Yang-Mills (at least as it seeems from the authors perspective). We do not go into any technical details or definitions here: most of these are well represented in the literature, for example [17]. (We also mention a survey article [15] of the author, in a somewhat similar vein, which contains more detail....