Phase Structure of Gauge Theories on an Interval

Understand

We discuss gauge symmetry breaking in a general framework of gauge theories on an interval.

• We first derive a possible set of boundary conditions for a scalar field, which are compatible with several consistency requirements.
• It is shown that with these boundary conditions the scalar field can acquire a nontrivial vacuum expectation value even if the scalar mass square is positive.
• Any nonvanishing vacuum expectation value cannot be a constant but, in general, depends on the extra dimensional coordinate of the interval.