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Context. The abundance inhomogeneities of light elements observed in GlobularClusters (GCs), and notably the ubiquitous Na-O anti-correlation, are generallyinterpreted as evidence that GCs comprise several generations of stars. Thereis an on-going debate as to the nature of the stars which produce theinhomogeneous elements, and investigating the behavior of several elements is away to shed new light on this problem. Aims. We aim at investigating the Li andNa content of the GC M 4, that is known to have a well defined Na-Oanti-correlation. Methods. We obtained moderate resolution (R=17 000-18 700)spectra for 91 main sequence (MS)/sub-giant branch stars of M 4 with theGiraffe spectrograph at the FLAMES/VLT ESO facility. Using model atmospheresanalysis we measured lithium and sodium abundances. Results. We detect a weakLi-Na anti-correlation among un-evolved MS stars. One star in the sample, #37934, shows the remarkably high lithium abundance A(Li)=2.87, compatible withcurrent estimates of the primordial lithium abundance. Conclusions. The shallowslope found for the Li-Na anti-correlation suggests that lithium is produced inparallel to sodium. This evidence, coupled with its sodium-rich nature,suggests that the high lithium abundance of star # 37934 may originate bypollution from a previous generations of stars. The recent detection of aLi-rich dwarf of pollution origin in the globular cluster NGC 6397 may alsopoint in this direction. Still, no clear cut evidence is available against apossible preservation of the primordial lithium abundance for star # 37934.

Lithium and sodium in the globular cluster M4. Detection of a Li-rich dwarf star: preservation or pollution?