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 the 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.
