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.

Low-scale string models, in which the string scale M s is of the order of TeV with large extra dimensions, can solve the problems of scale hierarchy and non-renormalizable quantum gravity in the standard model. String excited states of the standard model particles are possibly observed as resonances in the dijet invariant mass distribution at the LHC. There are two properties to distinguish whether the resonances are due to low-scale string or some other "new physics". One is a characteristic angular distribution in dijet events at the resonance due to spin degeneracy of string excited states, and the other is an appearance of the second resonance at a characteristic mass of second string excited states. We investigate a possibility to observe these evidences of low-scale string models by Monte Carlo simulations with a reference value of M s = 4 TeV at √ s = 14 TeV. It is shown that spin degeneracy at the dijet resonance can be observed by looking the χ-distribution with integrated luminosity of 20 fb −1 . It is shown that the second resonance can be observed at rather close to the first resonance in the dijet invariant mass distribution with integrated luminosity of 50 fb −1 . These are inevitable signatures of low-scale string models.

Low-scale string models are phenomenological models in String Theory, in which the string scale M s is of the order of TeV. String excited states which are characteristic modes in low-scale string models can be observed as resonances in dijet invariant mass distributions at the LHC. If a new heavy resonance is discovered at the LHC, it is important to investigate whether the resonance comes from low-scale string models. In this work, two analyses are performed: One is observing higher spin degeneracy of string excited states by an angular distribution analysis on the resonance, since the string resonance consists of several degenerate states with different spins. The other is observing second string excited states by a search for a second resonance in dijet invariant mass distributions, since second string excited states have characteristic masses of √ 2 times of masses of first string excited states. As the result of Monte Carlo simulations assuming the 14 TeV LHC, we give required luminosities for 5 σ confirmation in each analysis, in case of M s = 4.5, 4.75 and 5 TeV.1 It is pointed out in Ref.[8], for example, that light string excited states are possible even with a high string scale due to the warp effect in the Randall-Sundrum scenario.2 The Wigner d-function d J Jz,J z ′ (θ) represents an angular dependence of a process through a state with spin J, in which an initial state has total spin along z-axis, J z , and a final state has total spin along z ′ -axis, J z ′ . The angle θ is that between the z-axis and z ′ -axis.

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