Vacuum Topology of the Two Higgs Doublet Model
  We perform a systematic study of generic accidental Higgs-family and CP
symmetries that could occur in the two-Higgs-doublet-model potential, based on
a Majorana scalar-field formalism which realizes a subgroup of GL(8,C). We
derive the general conditions of convexity and stability of the scalar
potential and present analytical solutions for two non-zero neutral vacuum
expectation values of the Higgs doublets for a typical set of six symmetries,
in terms of the gauge-invariant parameters of the theory. By means of a
homotopy-group analysis, we identify the topological defects associated with
the spontaneous symmetry breaking of each symmetry, as well as the massless
Goldstone bosons emerging from the breaking of the continuous symmetries. We
find the existence of domain walls from the breaking of Z_2, CP1 and CP2
discrete symmetries, vortices in models with broken U(1)_PQ and CP3 symmetries
and a global monopole in the SO(3)_HF-broken model. The spatial profile of the
topological defect solutions is studied in detail, as functions of the
potential parameters of the two-Higgs doublet model. The application of our
Majorana scalar-field formalism in studying more general scalar potentials that
are not constrained by the U(1)_Y hypercharge symmetry is discussed. In
particular, the same formalism may be used to properly identify seven
additional symmetries that may take place in a U(1)_Y-invariant scalar
potential.
