  We propose a universal non-linear sigma model field theory for one
dimensional frustrated ferromagnets, which applies in the vicinity of a
"quantum Lifshitz point", at which the ferromagnetic state develops a spin wave
instability. We investigate the phase diagram resulting from perturbations of
the exchange and of magnetic field away from the Lifshitz point, and uncover a
rich structure with two distinct regimes of different properties, depending
upon the value of a marginal, dimensionless, parameter of the theory. In the
regime relevant for one dimensional systems with low spin, we find a
metamagnetic transition line to a vector chiral phase. This line terminates in
a critical endpoint from which emerges a cascade of multipolar phases. We show
that the field theory has the property of "asymptotic solubility", so that a
particular saddle point approximation becomes asymptotically exact near the
Lifshitz point. Our results provide an analytic framework for prior numerical
results on frustrated ferromagnets, and can be applied much more broadly.
