Constructing SU(N) fractional instantons

We study self-dual SU(N) gauge eld con gurations on the 4 torus with twisted boundary conditions, known as fractional instantons. Focusing on the minimum non-zero action case, we generalize the constant eld strength solutions discovered by `t Hooft and valid for certain geometries. For the general case, we construct the vector potential and eld strength in a power series expansion in a deformation parameter of the metric. The next to leading term is explicitly computed. The methodology is an extension of that used by the author for SU(2) fractional instantons and for vortices in two-dimensional Abelian Higgs models. Obviously, these solutions can also be seen as self-dual con gurations in R4 having a crystal structure, where each node of the crystal carries a topological charge of 1/NI acknowledge financial support from the MINECO/FEDER grant FPA2015-68541-P and the Spanish Agencia Estatal de Investigacion through the grant “IFT Centro de Excelencia Severo Ochoa SEV2016-0597” and the EU H2020-MSCA-ITN-2018-813942 (EuroPLEx

Scale setting for large-N SUSY Yang-Mills on the lattice

In this paper we study the large N limit of four-dimensional Supersymmetric Yang-Mills on the lattice using twisted reduced models. We have generated configurations with dynamical massive gluinos and various lattice ’t Hooft couplings, and verified that the Pfaffian remains positive. We have determined the lattice spacing in terms of various observables obtaining compatible results. Extrapolating to the massless gluino limit we obtain the lattice spacing dependence on the bare couplings for the supersymmetric theory. The observed dependence goes along the expected behaviour predicted by perturbation theoryThis work is partially supported by grant PGC2018-094857-B-I00 funded by MCIN/AEI/ 10.13039/501100011033 and by “ERDF A way of making Europe”, and by the Spanish Research Agency (Agencia Estatal de Investigación) through grants IFT Centro de Excelencia Severo Ochoa SEV-2016-0597 and No CEX2020-001007-S, funded by MCIN/AEI/10.13039 /501100011033. We also acknowledge support from the project H2020-MSCAITN-2018- 813942 (EuroPLEx) and the EU Horizon 2020 research and innovation programme, STRONG-2020 project, under grant agreement No 82409

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