CMB constraints on the fine structure constant

We study constraints on time variation of the fine structure constant alpha from cosmic microwave background (CMB) taking into account simultaneous change in alpha and the electron mass m_e which might be implied in unification theories. We obtain the constraints -0.097 < Delta alpha/alpha < 0.034 at 95% C.L. using WMAP data only, and -0.042 < Delta alpha/alpha < 0.026 combining with the constraint on the Hubble parameter by the HST Hubble Key Project. These are improved by 15% compared with constraints assuming only alpha varies. We discuss other relations between variations in alpha and m_e but we do not find evidence for varying alpha.