Effect of fermi surface curvature on low-energy properties of fermions with singular interactions

We discuss the effect of Fermi surface curvature on long-distance or time asymptotic behaviors of two-dimensional fermions interacting via a gapless mode described by an effective gauge-field-like propagator. By comparing the predictions based on the idea of multidimensional bosonization with those of the strong-coupling Eliashberg approach, we demonstrate that an agreement between the two requires a further extension of the former technique.