  We consider heat transfer across an arbitrary harmonic network connected to
two heat baths at different temperatures. The network has $N$ positional
degrees of freedom, of which $N_L$ are connected to a bath at temperature $T_L$
and $N_R$ are connected to a bath at temperature $T_R$. We derive an exact
formula for the cumulant generating function for heat transfer between the two
baths. The formula is valid even for $N_L \ne N_R$ and satisfies the
Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three
dimensions are known to exhibit different regimes of transport such as
ballistic, anomalous and diffusive, our result implies validity of the
fluctuation theorem in all regimes. Our exact formula provides a powerful tool
to study other properties of nonequilibrium current fluctuations.
