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 electronelectron 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. PACS numbers: 73.63.Fg, The experimental and theoretical studies of strong correlation effects are in the forefront of condensed matter research. Low-dimensional carbonaceous systems, fullerenes, carbon nanotubes (CNTs), and graphene exhibit a rich variety of such phenomena including superconductivity in alkali doped fullerenes [1], quantized transport in SWCNTs, and massless Dirac quasi-particles showing a half integer quantum Hall-effect in graphene even at room temperature [2]. A compelling correlated state of one-dimensional systems is the Luttinger liquid (LL) state. There is now abundant evidence from both theoretical [3,4,5,6,7] and experimental [8,9,10,11] side that the low energy properties of CNTs with a single shell, the single-wall carbon nanotubes (SWCNTs) can be described with the LL state. As a result, SWCNTs are regarded as a model system of the LL state, which could be exploited to further test the theories and novel experimental methods.Electron spin resonance (ESR) is a well established and powerful method to characterize correlated states of itinerant electrons. It helped to resolve e.g. the singlet nature of superconductivity in elemental metals [12], the magnetically ordered spin-density state in lowdimensional organic metals [13] and in alkali doped fullerides [14]. In three-dimensional metals, the ESR signal intensity is proportional to the Pauli spin-susceptibility, the ESR line-width and g-factor are determined by the mixing of spin up and down states due to spin-orbit (SO) coupling in the conduction band. These ESR measurables are affected when correlations are present and thus their study holds information about the nature of the correlated state.This motivated a decade long quest to find the ESR signal of itinerant electrons in SWCNTs and to characterize its properties in the framework of the expected correlations [15,16,17]. Detection of ESR in SWCNTs is also vital for applications as it enables to determine the spinlattice relaxation time, T 1 , which determines the usability for spintronics [18]. However, to our knowledge no conclusive evidence for this observation has been reported. An often cited argument for this anomalous absence of the ESR signal is the large heterogeneity of the system, the lack of crystallinity, and the pr...