Exact Exponents of Edge Singularities in Dynamic Correlation Functions of 1D Bose Gas

The spectral function and dynamic structure factor of bosons interacting by contact repulsion and confined to one dimension exhibit power-law singularities along the dispersion curves of the collective modes. We find the corresponding exponents exactly, by relating them to the known Bethe ansatz solution of the Lieb-Liniger model. Remarkably, the Luttinger liquid theory predictions for the exponents fail even at low energies, once the immediate vicinities of the edges are considered