International Journal of Modern Physics A

I discuss the basic elements of the process that will lead to the discovery of possible new phenomena at the LHC (Large Hadron Collider). We review the status of the tools available to model the Standard Model backgrounds, and the role that such tools can play in the discovery phase, and in the exploration of the features and parameters of such new phenomena.

Recent searches for physics beyond the Standard Model at high-energy colliders are reviewed, with emphasis on supersymmetry, additional space dimensions, extra gauge bosons, leptoquarks and model-independent searches. The results reported are based on data samples of up to 0.5 and 2.5 fb^-1 collected at HERA and at the Tevatron, respectively.

In the paper arXiv:0706.1618[hep-th], the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-3 tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R²-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.

In quantum gravity, we study the evolution of a two-dimensional planar open frozen spin network, in which the color (i.e. the twice spin of an edge) labeling edge changes but the underlying graph remains fixed. The mainly considered evolution rule, the random edge model, is depending on choosing an edge randomly and changing the color of it by an even integer. Since the change of color generally violate the gauge invariance conditions imposed on the system, detailed propagation rule is needed and it can be defined in many ways. Here, we provided one new propagation rule, in which the involved even integer is not a constant one as in previous works, but changeable with certain probability. In random edge model, we do find the evolution of the system under the propagation rule exhibits power-law behavior, which is suggestive of the self-organized criticality (SOC), and it is the first time to verify the SOC behavior in such evolution model for the frozen spin network. Furthermore, the increase of the average color of the spin network in time can show the nature of inflation for the universe.

It is shown how w_∞, w_1+∞ gauge field theory actions in 2D emerge directly from 4D gravity. Strings and membranes actions in 2D and 3D originate as well from 4D Einstein gravity after recurring to the nonlinear connection formalism of Lagrange–Finsler and Hamilton–Cartan spaces. Quantum gravity in 3D can be described by a W_∞ matrix model in D = 1 that can be solved exactly via the collective field theory method. We describe why a quantization of 4D gravity could be attained via a 2D quantum W_∞ gauge theory coupled to an infinite-component scalar-multiplet. A proof that noncritical W_∞ (super)strings are devoid of BRST anomalies in dimensions D = 27(D = 11), respectively, follows and which coincide with the critical (super)membrane dimensions D = 27(D = 11). We establish the correspondence between the states associated with the quasifinite highest weights irreducible representations of W_∞, algebras and the quantum states of the continuous Toda molecule. Schrödinger-like quantum mechanics wave functional equations are derived and solutions are found in the zeroth-order approximation. Since higher-conformal spin W_∞ symmetries are very relevant in the study of 2DW_∞ gravity, the quantum Hall effect, large N QCD, strings, membranes, … it is warranted to explore further the interplay among all these theories.

We furnish an algebraic understanding of the inequivalent connectivities (computed up to N ≤ 10) of the graphs associated to the irreducible supermultiplets of the N-extended supersymmetric quantum mechanics. We prove that the inequivalent connectivities of the N = 5 and N = 9 irreducible supermultiplets are due to inequivalent decompositions into two sets of N = 4 (respectively, N = 8) supermultiplets. "Oxido-reduction" diagrams linking the irreducible supermultiplets of the N = 5, 6, 7, 8 supersymmetries are presented. We briefly discuss these results and their possible applications.

We comment on the brane solutions for the boundary model that have been proposed so far and point out that they should be distinguished according to the patterns regular/irregular and discrete/continuous. In the literature, mostly irregular branes have been studied, while results on the regular ones are rare. For all types of branes, there are questions about how a second factorization constraint in the form of a b^-2/2-shift equation can be derived. Here, we assume analyticity of the boundary two-point function, which means that the Cardy–Lewellen constraints remain unweakened. This enables us to derive unambiguously the desired b^-2/2-shift equations. They serve as important additional consistency conditions. For some regular branes, we also derive 1/2-shift equations that were not known previously. Case by case, we discuss possible solutions to the enlarged system of constraints. We find that the well-known irregular continuous AdS₂ branes are consistent with our new factorization constraint. Furthermore, we establish the existence of a new type of brane: the shift equations in a certain regular discrete case possess a nontrivial solution that we write down explicitly. All other types are found to be inconsistent when using our second constraint. We discuss these results in view of the Hosomichi–Ribault proposal and some of our earlier results on the derivation of b^-2/2-shift equations.

The nature of scalar wave functions near the horizon of Reissner–Nordstrom (RN) extremal and Schwarzschild–de Sitter (SdS) extremal black holes are found using WKB approximation and the effect of reflection of waves from the horizon. The absorption cross-section σ_abs when RN extremal and SdS extremal black holes placed in a Klein–Gordon field is calculated.

Dirac showed that the existence of one magnetic pole in the universe could offer an explanation of the discrete nature of the electric charge. Magnetic poles appear naturally in most grand unified theories. Their discovery would be of greatest importance for particle physics and cosmology. The intense experimental search carried thus far has not met with success. I propose a universe with magnetic poles which are not observed free because they hide in deeply bound monopole–antimonopole states named monopolium. I discuss the realization of this proposal and its consistency with known cosmological features. I furthermore analyze its implications and the experimental signatures that confirm the scenario.

We study the large branching ratios of B→ηK* decays and the time-dependent CP asymmetry S_ϕKS anomaly of B→ϕK_S decay in a flavor changing Z′ model associated with flavor changing neutral currents at the tree level. Considering the right-handed flavor changing couplings and setting ξ^LL = ξ^RL = ξ^LR = ξ^RR = ξ, we obtain 0.011 < ξ < 0.0131, this parameter region could give a simultaneous explanation to these anomalies of B→ηK* and B→ϕK_S decays. The results are consistent with the constraints and the assumptions of some references.

For systems with a finite number of degrees of freedom, it is shown in a paper [Commun Math. Phys.254, 167 (2005), arXiv:hep-th/0303014] that first-class constraints are Abelianizable if the Faddeev–Popov determinant is not vanishing for some choice of subsidiary constraints. Here, for irreducible first-class constraint systems with SO(3) or SO(4) gauge symmetries, including a subset of coordinates in the fundamental representation of the gauge group, we explicitly determine the Abelianizable and non-Abelianizable classes of constraints. For the Abelianizable class, we explicitly solve the constraints to obtain the equivalent set of Abelian first-class constraints. We show that for non-Abelianizable constraints there exist residual gauge symmetries which results in confinement-like phenomena.