  P-term inflation is a version of hybrid inflation which naturally appears in
some brane inflation models. It was introduced in the framework of N=2
supersymmetric gauge theory where superconformal SU(2,2|2) symmetry is broken
down to N=2 supersymmetry by the vev of the auxiliary triplet field P.
Depending on the direction of this vev, one can get either D-term inflation or
F-term inflation with a particular relation between Yukawa and gauge coupling,
or a mix of these models. We show that F and D models, before coupling to
gravity is included, are related by a change of variables. Coupling of this
model to N=1 supergravity breaks this symmetry and introduces a class of P-term
models interpolating between D-term and F-term inflation. The difference
between these models is determined by the direction of the vector P, which
depends on the fluxes in the underlying D3/D7 model of brane inflation. We
discuss cosmological consequences of various versions of P-term inflation.
