Tunneling in Quantum Wires: a Boundary Conformal Field Theory Approach

Tunneling through a localized barrier in a one-dimensional interacting electron gas has been studied recently using Luttinger liquid techniques. Stable phases with zero or unit transmission occur, as well as critical points with universal fractional transmission whose properties have only been calculated approximately, using a type of ``$\epsilon$-expansion''. It may be possible to calculate the universal properties of these critical points exactly using the recent boundary conformal field theory technique, although difficulties arise from the $\infty$ number of conformal towers in this $c=4$ theory and the absence of any apparent ``fusion'' principle. Here, we formulate the problem efficiently in this new language, and recover the critical properties of the stable phases.