  We present electric dipole polarizabilities ($\alpha_d$) of the alkali-metal
negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic
many-body methods. Differences in the results are shown by considering
Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and
DC Hamiltonian with the lower-order quantum electrodynamics interactions. At
first, these interactions are included self-consistently in the
Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are
incorporated over the DHF wave functions in the second-order many-body
perturbation theory, random phase approximation and coupled-cluster (CC)
theory. Roles of electron correlation effects and relativistic corrections are
analyzed using the above many-body methods with size of the ions. We finally
quote precise values of $\alpha_d$ of the above negative ions by estimating
uncertainties to the CC results, and compare them with other calculations
wherever available.
