We compute by supersymmetric localization the expectation values of half-bps't~hooft line operators in and gauge theories on with an we evaluate the nonperturbative contributions due to monopole screening by calculating the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the't~hooft operators using branes and orientifolds in type ii string theories.we compute by supersymmetric localization the expectation values of half-bps't~hooft line operators in and gauge theories on with an we evaluate the non-perturbative contributions due to monopole screening by calculating the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the't~hooft operators using branes and orientifolds in type ii string theories.