  We unveil a remarkable connection between the sine-Gordon quantum field
theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the
non-relativistic limit of the two point correlation function of the sine-Gordon
theory is related to the generating function of the height distribution of the
KPZ field with droplet initial conditions, i.e. the directed polymer free
energy with two endpoints fixed. As shown recently, the latter can be expressed
as a Fredholm determinant which in the large time separation limit converges to
the GUE Tracy-Widom cumulative distribution. Possible applications and
extensions are discussed.
