FK/Fπ from Mobius domain-wall fermions solved on gradient-flowed HISQ ensembles

We report the results of a lattice quantum chromodynamics calculation of F-K/F-pi using Mobius domain-wall fermions computed on gradient-flowed N-f = 2 + 1 + 1 highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from 130 less than or similar to m(pi) less than or similar to N 400 MeV, four lattice spacings of a similar to 0.15, 0.12, 0.09 and 0.06 fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the a similar to 0.06 fm ensemble is helpful, but not necessary to achieve a subpercent determination of F-K/F pi. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of F (K) over cap+/F (pi) over cap + = 1.1942(45) with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of vertical bar V-us vertical bar/vertical bar V-ud vertical bar= 0.2311(10).