  We propose a realisation of 'new inflation' in supergravity (SUGRA), where
the flatness of the inflaton potential is protected by a Heisenberg symmetry.
Inflation can be associated with a particle physics phase transition, with the
inflaton being a (D-flat) direction of Higgs fields which break some symmetry
at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour
symmetry breaking. This is possible since compared to a shift symmetry, which
is usually used to protect a flat inflaton potential, the Heisenberg symmetry
is compatible with a (gauge) non-singlet inflaton field. In contrast to
conventional new inflation models in SUGRA, where the predictions depend on
unknown parameters of the K"ahler potential, the model with Heisenberg symmetry
makes discrete predictions for the primordial perturbation parameters which
depend only on the order n at which the inflaton appears in the effective
superpotential. The predictions for the spectral index n_s can be close to the
best-fit value of the latest Planck 2013 results.
