Quantum avoidance of G\"{o}del's closed timelike curves

In a large class of nonlocal as well as local higher derivative theories minimally coupled to the matter sector, we investigate the exactness of two different classes of homogeneous G\"{o}del-type solutions, which may or may not allow closed time-like curves (CTC). Our analysis is limited to spacetimes solving the Einstein's EoM, thus we can not exclude the presence of other G\"{o}del-type solutions solving the EoM of local and nonlocal higher derivative theories but not the Einstein's EoM.It turns out that the homogeneous G\"{o}del spacetimes without CTC are basically exact solutions for all theories, while the metrics with CTC are not exact solutions of (super-)renormalizable local or nonlocal gravitational theories. Hence, the quantum renormalizability property excludes theories suffering of the G\"{o}del's causality violation. We also comment about nonlocal gravity non-minimally coupled to matter. In this class of theories, all the G\"{o}del's spacetimes, with or without CTC, are exact solutions at classical level. However, the quantum corrections, although perturbative, very likely spoil the exactness of such solutions. Therefore, we can state that the G\"{o}del's Universes with CTC and the super-renormalizability are mutually exclusive.