Higgs Mechanism in Nonlocal Field Theories
  We study spontaneous gauge symmetry breaking and the Higgs mechanism in
nonlocal field theories. Motivated by the level truncated action of string
field theory, we consider a class of nonlocal field theories with an
exponential factor of the d'Alembertian attached to the kinetic and mass terms.
Modifications of this kind are known to make mild the UV behavior of loop
diagrams and thus have been studied not only in the context of string theory
but also as an alternative approach to quantum gravity. In this paper we argue
that such a nonlocal theory potentially includes a ghost mode near the nonlocal
scale in the particle spectrum of the symmetry broken phase. This is in sharp
contrast to local field theories and would be an obstruction to making a simple
nonlocal model a UV complete theory. We then discuss a possible way out by
studying nonlocal theories with extra symmetries such as gauge symmetries in
higher spacetime dimensions.
