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We consider a 1D Bose gas with attractive interactions in anout-of-equilibrium highly excited state containing no bound states. We showthat relaxation processes in the gas are suppressed, making the systemmetastable on long timescales. We compute dynamical correlation functions,revealing the structure of excitations, an enhancement of umklapp correlationsand new branches due to intermediate bound states. These features give a clearindication of the attractive regime and can be probed experimentally. Weobserve that, despite its out-of-equilibrium nature, the system displayscritical behaviour: correlation functions are characterised by asymptoticpower-law decay described by the Luttinger liquid framework.

Metastable criticality and the super Tonks-Girardeau gas