  We consider a quantum wire with two subbands of spin-polarized electrons in
the presence of strong interactions. We focus on the quantum phase transition
when the second subband starts to get filled as a function of gate voltage.
Performing a one-loop renormalization group (RG) analysis of the effective
Hamiltonian, we identify the critical fixed-point theory as a conformal field
theory having an enhanced SU(2) symmetry and central charge 3/2. While the
fixed point is Lorentz invariant, the effective 'speed of light' nevertheless
vanishes at low energies due to marginally irrelevant operators leading to a
diverging critical specific heat coefficient.
