  We present exact results for the electrical and thermal conductivity and
Seebeck coefficient at low temperatures and frequencies in the quantum-critical
region for fermions on a lattice scattering with the collective fluctuations of
the quantum xy model. This is done by the asymptotically exact solution of the
vertex equation in the Kubo formula for these transport properties. The model
is applicable to the fluctuations of the loop-current order in cuprates as well
as to a class of quasi-two dimensional heavy-fermion and other metallic
antiferromagnets, and proposed recently also for the possible loop-current
order in Moir\'{e} twisted bi-layer graphene and bi-layer WSe$_2$. All these
metals have a linear in temperature electrical resistivity in the
quantum-critical region of their phase diagrams, often termed "Planckian"
resistivity. The solution of the integral equation for the vertex in the Kubo
equation for transport shows that all vertex renormalizations except due to
Aslamazov-Larkin processes are absent. The latter appear as an Umklapp
scattering matrix, which is shown to give only a temperature independent
multiplicative factor for electrical resistivity which is non-zero in the pure
limit only if the Fermi-surface is large enough, but do not affect thermal
conductivity. We also show that the mass renormalization which gives a
logarithmic enhancement of the marginal Fermi-liquid specific heat does not
appear in the electrical resistivity as well as in the thermal conductivity. On
the other hand the mass renormalization appears in the Seebeck coefficient. The
results for transport properties are derived for any Fermi-surface on any
lattice. As an example, the linear in $T$ electrical resistivity is explicitly
calculated for large enough circular Fermi-surfaces on a square lattice. We
also discuss in detail the conservation laws that play a crucial role in all
transport properties.
