  A search is presented for physics beyond the standard model (SM) using
electron or muon pairs with high invariant mass. A data set of proton-proton
collisions collected by the CMS experiment at the LHC at $\sqrt{s}=$ 13 TeV
from 2016 to 2018 corresponding to a total integrated luminosity of up to 140
fb$^{-1}$ is analyzed. No significant deviation is observed with respect to the
SM background expectations. Upper limits are presented on the ratio of the
product of the production cross section and the branching fraction to dileptons
of a new narrow resonance to that of the Z boson. These provide the most
stringent lower limits to date on the masses for various spin-1 particles,
spin-2 gravitons in the Randall--Sundrum model, as well as spin-1 mediators
between the SM and dark matter particles. Lower limits on the ultraviolet
cutoff parameter are set both for four-fermion contact interactions and for the
Arkani-Hamed, Dimopoulos, and Dvali model with large extra dimensions. Lepton
flavor universality is tested at the TeV scale for the first time by comparing
the dimuon and dielectron mass spectra. No significant deviation from the SM
expectation of unity is observed.
