  We calculate holographically three-point functions of scalar operators with
large dimensions at finite density and finite temperature. To achieve this, we
construct new solutions that involve two isometries of the deformed internal
space. The novel feature of these solutions is that the corresponding two-point
function depends not only on the conformal dimension but also on the difference
between the two angular momenta. After identifying the dual operators, we
systematically calculate three-point correlators as an expansion in powers of
the temperature and the chemical potential. Our analytic perturbative results
are in agreement with the exact numerical computation. The three point
correlator (when the background contains either temperature or density but not
both) is always a monotonic function of the temperature or the chemical
potential. However, when both parameters are present the three point correlator
is no longer a monotonic function. For fixed finite temperature and small
values of the chemical potential a minimum of the three-point function appears.
Surprisingly, contributions from the internal space do not depend on the
chemical potential or the temperature, as long as those are treated as
perturbations.
