We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi-one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature, our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground state of the repulsive Lieb-Liniger gas, to the super-Tonks-Girardeau state. At finite temperature, we obtain that the three-body correlator has a weak dependence on temperature up to the degeneracy temperature
TD. We also find that, for temperatures larger than
TD, the values of the three-body correlator for the super-Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar, even for relatively small couplings.