  A comprehensive theory of electron spin resonance (ESR) for a Luttinger
liquid (LL) state of correlated metals is presented. The ESR measurables such
as the signal intensity and the line-width are calculated in the framework of
Luttinger liquid theory with broken spin rotational symmetry as a function of
magnetic field and temperature. We obtain a significant temperature dependent
homogeneous line-broadening which is related to the spin symmetry breaking and
the electron-electron interaction. The result crosses over smoothly to the ESR
of itinerant electrons in the non-interacting limit. These findings explain the
absence of the long-sought ESR signal of itinerant electrons in single-wall
carbon nanotubes when considering realistic experimental conditions.
