We study the Maxwell–Einstein theory in the framework of effective field theories. We show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a Lee–Wick vector field as an extra degree of freedom in the theory. Thus gravity provides a natural mechanism for the emergence of this exotic particle.

We construct a fully back-reacted holographic dual of a four-dimensional field theory which exhibits chiral symmetry breaking. Two possible models are considered by studying the effects of a five-dimensional field, dual to the qq operator. One model has smooth geometry at all radii and the other dynamically generates a cutoff at finite radius. Both of these models satisfy Einstein's field equations. The second model has only three free parameters, as in QCD, and we show that this gives phenomenologically consistent results. We also discuss the possibility that in order to obtain linear confinement from a back-reacted model it may be necessary to consider the condensate of a dimension two operator.

A new economical way to understand neutrino mixings in the seesaw framework is proposed. We argue that its origin can be understood within the seesaw framework by a hidden condition on the mass matrix of heavy right-handed neutrinos under the transformation of the Abelian finite group Z(3) on the flavor basis. Ignoring CP phases, we show that it can lead to the generic form of the effective light neutrino mass matrix from which the Harrison-Perkins-Scott mixing matrix appears naturally, as well as an experimentally allowed nonzero sin theta(13). Two examples are given to illustrate that the mass matrix based on our proposal is in good agreement with the current experimental data.

We embed the flipped SU(5) models into the SO(10) models. After the SO(10) gauge symmetry is broken down to the flipped SU(5) x U(1)(X) gauge symmetry, we can split the five/one-plets and ten-plets in the spinor 16 and 16 Higgs fields via the stable sliding singlet mechanism. As in the flipped SU(5) models, these ten-plet Higgs fields can break the flipped SU(5) gauge symmetry down to the Standard Model gauge symmetry. The doublet-triplet splitting problem can be solved naturally by the missing partner mechanism, and the Higgsino-exchange mediated proton decay can be suppressed elegantly. Moreover, we show that there exists one pair of the light Higgs doublets for the electroweak gauge symmetry breaking. Because there exist two pairs of additional vector-like particles with similar intermediate-scale masses, the SU(5) and U(1)(X) gauge couplings can be unified at the GUT scale which is reasonably (about one or two orders) higher than the SU(2)(L) x SU(3)(C) unification scale. Furthermore, we briefly discuss the simplest SO(10) model with flipped SU(5) embedding, and point out that it can not work without fine-tuning.

Building on recent research into five-dimensional holographic models of QCD, we extend this work by including the strange quark with an SU(3)L × SU(3)R gauge symmetry in the five-dimensional theory. In addition we deform the naive AdS metric with a single parameter, thereby breaking the conformal symmetry at low energies. The vector and axial vector sectors are studied in detail and both the masses and decay constants are calculated with the additional parameters. It is shown that with a single extra degree of freedom, exceptional agreement with experimental results can be obtained in the light quark sector while the kaon sector of the vector and axial vector octet is found to give around 10% agreement with lattice results. We propose some simple extensions to this work to be taken up in future research.