Abstract
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.
Highlights
JHEP08(2018)[064] model building of particle physics, the recombination process of D-branes provides a natural realization of the Standard Model Higgs mechanism [10]
In this paper we studied spontaneous gauge symmetry breaking and the Higgs mechanism in a class of nonlocal gauge theories
We found that the nonlocality drastically changes the particle spectrum in the symmetry broken phase, to the open string tachyon condensation case
Summary
In string theory, this situation is interpreted as the disappearance of open string excitations in the tachyon vacuum due to decay of unstable D-branes [7–9]. This situation is interpreted as the disappearance of open string excitations in the tachyon vacuum due to decay of unstable D-branes [7–9] In this regime, there are two real solutions to fλ(x) = 0, which correspond to two types of physical particle excitations with the on-shell conditions,. Particle excitations (λ > λ∗), (b) there appears an undesired ghost mode near the nonlocal scale (0 < λ < λ∗) The latter situation will be problematic if we would like to think of the nonlocal field theory as a UV complete theory, even though there is no problem as long as we regard it, e.g., as a toy model for string field theory or an effective field theory with a cutoff below the mass scale of the ghost. In the rest of this paper, we extend the argument to the Higgs mechanism in nonlocal gauge theories and discuss if it is possible to have a massive gauge boson in a consistent way
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