  We study twist operators in higher dimensional CFT's. In particular, we
express their conformal dimension in terms of the energy density for the CFT in
a particular thermal ensemble. We construct an expansion of the conformal
dimension in power series around n=1, with n being replica parameter. We show
that the coefficients in this expansion are determined by higher point
correlations of the energy-momentum tensor. In particular, the first and second
terms, i.e. the first and second derivatives of the scaling dimension, have a
simple universal form. We test these results using holography and free field
theory computations, finding agreement in both cases. We also consider the
`operator product expansion' of spherical twist operators and finally, we
examine the behaviour of correlators of twist operators with other operators in
the limit n ->1.
