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We use a lattice determination of the hadronic vacuum polarization tensor tostudy the associated Ward identities and compute the Adler function. The vacuumpolarization tensor is computed from a combination of point-split and localvector currents, using two flavours of O($a$)-improved Wilson fermions.Partially twisted boundary conditions are employed to obtain a fine momentumresolution. The modifications of the Ward identities by lattice artifacts andby the use of twisted boundary conditions are monitored. We determine the Adlerfunction from the derivative of the vacuum polarization function over a largeregion of momentum transfer $q^2$. As a first account of systematic effects, acontinuum limit scaling analysis is performed in the large $q^2$ regime.

Computing the Adler function from the vacuum polarization function