International Journal of Modern Physics A

A summary is reported on our previous publications about four-dimensional supersymmetric Spin(10) gauge theory with chiral superfields in the spinor and vector representations in the non-Abelian Coulomb phase. Carrying out the method of a-maximization, we studied decoupling operators in the infrared and the renormalization flow of the theory. We also give a brief review on the non-Abelian Coulomb phase of the theory after recalling the unitarity bound and the a-maximization procedure in four-dimensional conformal field theory.

The existing data appear to provide hints of an underlying high scale theory. These arise from the gauge coupling unification, from the smallness of the neutrino masses, and via a nonvanishing muon anomaly. An overview of high scale models is given with a view to possible tests at the Large Hadron Collider. Specifically we discuss here some generic approaches to deciphering their signatures. We also consider an out of the box possibility of a four-generation model where the fourth generation is a mirror generation rather than a sequential generation. Such a scenario can lead to some remarkably distinct signatures at the LHC.

Saturation in deep inelastic scattering and deeply virtual Compton scattering is associated with a phase transition between the partonic gas, typical of moderate x and Q², and partonic fluid appearing at increasing Q² and decreasing Bjorken x. In this paper we do not intend to propose another parametrization of the structure function; instead we suggest a new insight into the internal structure of the nucleon, as seen in deep inelastic scattering, and its connection with that revealed in high-energy nucleons and heavy-ion collisions.

The AdS/QCD models are known to be closely related to the QCD sum rules in the large-N_c (called also planar) limit. Rewriting the theory of infinite tower of free stable mesons expected in the large-N_c QCD as a five-dimensional theory, we scrutinize to what extend the bottom-up holographic models may be viewed as an alternative language expressing the phenomenology of planar QCD sum rules. It is found that many features of AdS/QCD models can be thereby obtained without invoking prescriptions from the original AdS/CFT correspondence. Under some assumptions, all possibilities leading to simple Regge trajectories are classified, and it is argued that the most phenomenologically consistent model is the one called "soft wall model" in the holographic approach, with a preference to the positive-sign dilaton background.

When one uses the Coleman–Weinberg renormalization condition, the effective potential V in the massless theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the (p + 1) order renormalization group function determine the sum of all the N^pLL order contribution to V to all orders in the loop expansion. We discuss here how, in addition to fixing the N^pLL contribution to V, the (p + 1) order renormalization group functions can also be used to determine portions of the N^p+nLL contributions to V. When these contributions are summed to all orders, the singularity structure of V is altered. An alternate rearrangement of the contributions to V in powers of ln ϕ, when the extremum condition V′(ϕ = v) = 0 is combined with the renormalization group equation, show that either v = 0 or V is independent of ϕ. This conclusion is supported by showing the LL, …, N⁴LL contributions to V become progressively less dependent on ϕ.

We present a new classical generalized one-monopole solution of the SU(2) Yang–Mills–Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with θ-winding number m = 1 and ϕ-winding number n = 1 is an axially symmetric Jacobi elliptic generalization of the 't Hooft–Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft–Polyakov one-monopole to the Jacobi elliptic functions and solving the second-order equations of motion numerically when the Higgs potential is vanishing and nonvanishing. These solutions are regular non-BPS finite energy solutions.

We argue that Poincaré symmetry can be implemented in noncommutative field theory (NCFT) if we allow the parameter of noncommutative deformation θ^μν to change as a two-tensor under the corresponding space–time symmetry. The implementation is consistent with the definition of θ^μν in terms of space–time coordinates and with the Moyal star product. Inspired by the standard definition of a variational symmetry we found a universal way to correct the implementation of the Poincaré symmetry by a term proportional to the variation of θ^μν in such a way that the new transformation define a symmetry of the theory. Finally we present as an example the case of NCYM theory and comment about the obstructions to implement generalized space–time symmetries in NCFT-like conformal or diffeomorphism transformations.

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices.

The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.