We treat the fluctuations of non-Abelian gauge fields around a classical configuration by means of a transformation from the Yang-Mills gauge field to a homogeneously transforming field variable. We use the formalism to compute the effective action induced by these fluctuations in a static background without Wu-Yang ambiguity.

Traditional ideas for testing unification involve searching for the decay of the proton and its branching modes. We point out that several astrophysical experiments are now reaching sensitivities that allow them to explore supersymmetric unified theories. In these theories the electroweak-mass dark matter particle can decay, just like the proton, through dimension 6 operators with lifetime $\sim {10}^{26}\mathrm{s}$. Interestingly, this time scale is now being investigated in several experiments including ATIC, PAMELA, HESS, and Fermi. Positive evidence for such decays may be opening our first direct window to physics at the supersymmetric unification scale of $M_{\mathrm{GUT}}\sim {10}^{16}\mathrm{GeV}$, as well as the TeV scale. Moreover, in the same supersymmetric unified theories, dimension 5 operators can lead a weak-scale superparticle to decay with a lifetime of $\sim 100\mathrm{s}$. Such decays are recorded by a change in the primordial light element abundances and may well explain the present discord between the measured Li abundances and standard big bang nucleosynthesis, opening another window to unification. These theories make concrete predictions for the spectrum and signatures at the LHC as well as Fermi.

Examples of test electromagnetic waves on a Friedmann-Lemaître-Robertson-Walker (FLRW) background are constructed from explicit perturbations of the FLRW space-times describing gravitational waves propagating in the isotropic universes. A possible physical mechanism for the production of the test electromagnetic waves is shown to be the coupling of the gravitational waves with a test magnetic field, confirming the observation of Marklund, Dunsby and Brodin [Phys. Rev. D 62, 101501(R) (2000)].

Gravitational properties of a hedgehog-type topological defect in two extra dimensions are considered in general relativity employing a vector as the order parameter. The developed macroscopic theory of phase transitions with spontaneous symmetry breaking is applied to the analysis of possible “thick” brane structures. The previous considerations were done using the order parameter in the form of a multiplet in a target space of scalar fields. The difference of these two approaches is analyzed and demonstrated in detail. There are two different symmetries of regular solutions of Einstein equations for a hedgehog-type vector order parameter. Both solutions are analyzed in parallel analytically and numerically. Regular configurations in cases of a vector order parameter have one more free parameter in comparison with the scalar multiplet solutions. It is shown that the existence of a negative cosmological constant is sufficient for the spontaneous symmetry breaking of the initially plain bulk. Regular configurations have a growing gravitational potential and are able to trap the matter to the brane. Among others there are solutions with the gravitational potential having several points of minimum such as being identical in the uniform bulk spinless particles, being trapped within separate points of minimum, acquiring different masses, and appearing to an observer within the brane as different particles with integer spins.

We search for simultaneous baryon and lepton number violating decays of the $D^0$ meson. Specifically, we use $281{\mathrm{pb}}^{-1}$ of data taken on the $\psi (3770)$ resonance with the CLEO-c detector at the CESR collider to look for decays $D^0\to \overline{p}{e}^{+}$, ${\overline{D}}^0\to \overline{p}{e}^{+}$, $D^0\to p{e}^{-}$, and ${\overline{D}}^0\to p{e}^{-}$. We find no significant signals and set the following branching fraction upper limits: $D^0\to \overline{p}{e}^{+}({\overline{D}}^0\to \overline{p}{e}^{+})<1.1\times {10}^{-5}$ and $D^0\to p{e}^{-}({\overline{D}}^0\to p{e}^{-})<1.0\times {10}^{-5}$, both at the 90% confidence level.

We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam’s prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with $CP$ conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.

We propose a dark matter model with standard model singlet extension of the universal extra dimension model to explain the recent observations of ATIC, PPB-BETS, PAMELA, and DAMA. Other than the standard model fields propagating in the bulk of a five-dimensional space, one fermion field and one scalar field are introduced and both are standard model singlets. The zero mode of the new fermion is identified as the right-handed neutrino, while its first Klein-Kaluza (KK) mode is the lightest KK-odd particle and the dark matter candidate. The cosmic ray spectra from ATIC and PPB-BETS determine the dark matter particle mass and hence the fifth dimension compactification scale to be 1.0–1.6 TeV. The zero mode of the singlet scalar field with a mass below 1 GeV provides an attractive force between dark matter particles, which allows a Sommerfeld enhancement to boost the annihilation cross section in the Galactic halo to explain the PAMELA data. The DAMA annual modulation results are explained by coupling the same scalar field to the electron via a higher-dimensional operator. We analyze the model parameter space that can satisfy the dark matter relic abundance and accommodate all the dark matter detection experiments. We also consider constraints from the diffuse extragalactic gamma-ray background, which can be satisfied if the dark matter particle and the first KK mode of the scalar field have highly degenerate masses.

We report the first calculation of the simplest but most fundamental transverse-momentum-dependent distribution of quarks in the nucleon, i.e. the time-reversal-even unpolarized transverse-momentum-dependent quark and antiquark distribution with isoscalar combination, within the framework of the chiral quark soliton model. The nonperturbative account of the deformed Dirac-sea quarks within the theoretical scheme enables us to make reliable predictions not only for the quark distribution but also for the antiquark distribution. We found that the predicted average transverse momentum square $⟨k_{\perp }^2⟩$ of quarks and antiquarks depends strongly on their longitudinal momentum fraction $x$, which means that the frequently used assumption of factorization in $x$ and $k_{\perp }$ is significantly violated. It is also found, somewhat unexpectedly, that the average transverse momentum square of antiquarks is considerably larger than that of quarks.

In this article, we study the mass spectrum of the scalar hidden charm and bottom tetraquark states with the QCD sum rules. The numerical results are compared with the corresponding ones from a relativistic quark model based on a quasipotential approach in QCD. The relevant values from the constituent diquark model based on the constituent diquark masses and the spin-spin interactions are also discussed.

We investigate the viability of thermal leptogenesis in type-I seesaw models with leptonic flavor symmetries that lead to tribimaximal neutrino mixing. We consider an effective theory with an $A_4\times Z_3\times Z_4$ symmetry, which is spontaneously broken at a scale much higher than the electroweak scale. At the high scale, leptonic Yukawa interactions lead to exact tribimaximal mixing and the heavy Majorana neutrino mass spectrum is exactly degenerate. In this framework, leptogenesis becomes viable once this degeneracy is lifted either by renormalization group effects or by a soft breaking of the $A_4$ symmetry. The implications for low-energy neutrino physics are discussed.

In this work, a new ansatz is introduced to make the calculations of the metric operator in pseudo-Hermitian field theory simpler. The idea is to assume that the metric operator is not only a functional of the field operator $\varphi$ and its conjugate field $\pi$ but also on the field gradient $\nabla \varphi$. The ansatz enables one to calculate the metric operator just once for all dimensions of the space-time. We calculated the metric operator of the $i{\varphi }^3$ scalar field theory up to first order in the coupling. The higher orders can be conjectured from their corresponding operators in the quantum mechanical case available in the literature. We assert that the calculations existing in literature for the metric operator in field theory are cumbersome and are done case by case concerning the dimension of space-time in which the theory is investigated. In fact, with the aid of this work a rigorous study of a $\mathcal{P}\mathcal{T}$-symmetric Higgs mechanism can be reached.

It is shown that observers in the standard ADM $3+1$ treatment of matter are the same as the observers used in the matter treatment of Bondi: they are comoving and local Minkowskian. Bondi’s observers are the basis of the post-quasistatic approximation (PQSA) to study a contracting distribution of matter. This correspondence suggests the possibility of using the PQSA as a test bed for numerical relativity. The treatment of matter by the PQSA and its connection with the ADM $3+1$ treatment are presented, for its practical use as a calibration tool and as a test bed for numerical relativistic hydrodynamic codes.

We study a simple version of the AdS/CFT correspondence, where operators have integer conformal dimensions. In this model, bulk causality follows from boundary analyticity, even in nontrivial black hole backgrounds that break the underlying conformal symmetry. This allows a natural set of quasilocal bulk observables to be constructed. Estimates of finite central charge corrections to semiclassical correlators are made. These corrections are used to determine the regime of validity of effective field theory in the bulk spacetime. The results are consistent with black hole complementarity.

Motivated by the isomorphism between $osp(4|6)$ superalgebra and $D=3$ $\mathcal{N}=6$ superconformal algebra we consider the superstring action on the ${\mathrm{AdS}}_4\times \mathbb{C}{\mathbb{P}}^3$ background parametrized by $D=3$ $\mathcal{N}=6$ super-Poincare and ${\mathbb{C}\mathbb{P}}^3$ coordinates supplemented by the coordinates corresponding to dilatation and superconformal generators. The relation between the degeneracy of fermionic equations of motion and the action $\kappa$-invariance in the framework of the supercoset approach is also discussed.

We take a first step towards the solution of QCD in $1+1$ dimensions at nonzero density. We regularize the theory in the UV by using a lattice and in the IR by putting the theory in a box of spatial size $L$. After fixing to axial gauge we use the coherent states approach to obtain the large-$N$ classical Hamiltonian $\mathcal{H}$ that describes color neutral quark-antiquark pairs interacting with spatial Polyakov loops in the background of baryons. Minimizing $\mathcal{H}$ we get a regularized form of the ‘t Hooft equation that depends on the expectation values of the Polyakov loops. Analyzing the $L$ dependence of this equation we show how volume independence, à la Eguchi and Kawai, emerges in the large-$N$ limit, and how it depends on the expectation values of the Polyakov loops. We describe how this independence relies on the realization of translation symmetry, in particular, when the ground state contains a baryon crystal. Finally, we remark on the implications of our results on studying baryon density in large-$N$ QCD within single-site lattice theories and on some general lessons concerning the way four-dimensional large-$N$ QCD behaves in the presence of baryons.

We investigate the cosmological perturbations in generalized gravity, where the Ricci scalar and a scalar field are nonminimally coupled via an arbitrary function $f(\phi ,R)$. In the Friedmann-Lemaître-Robertson-Walker background, by studying the linear perturbation theory, we separate the scalar-type perturbations into the curvature perturbation and the entropy perturbation, whose evolution equations are derived. Then we apply this framework to inflation. We consider the generalized slow-roll conditions and the quantization initial condition. Under these conditions, two special examples are studied analytically. One example is the case with no entropy perturbation. The other example is a model with the entropy perturbation large initially but decaying significantly after crossing the horizon.

We analyze the behavior of linear perturbations in vector inflation. In contrast to scalar field inflation, the linearized theory with vector fields contains couplings between scalar, vector, and tensor modes. The perturbations decouple only in the ultraviolet limit, which allows us to carry out the canonical quantization. Superhorizon perturbations can be approximately analyzed due to suppressed mixing between different modes in the small field models. We find that the vector perturbations of the metric decay exponentially, but the scalar and tensor modes could remain weakly coupled throughout the evolution. As a result, vector inflation can produce significant correlations of the scalar and tensor modes in the CMB. For realistic models the effect is rather small, but not negligible.

We explore the sparticle and Higgs spectroscopy of an SU(5) inspired extension of the constrained minimal supersymmetric standard model. The universal soft parameter $m_0$ is replaced by $m_{\overline{5}}$ and $m_{10}$, where $m_{\overline{5}}$ and $m_{10}$ denote universal soft scalar masses associated with fields in the five- and ten-dimensional representations of SU(5). The special case $m_{\overline{5}}\ll m_{10}$ yields a rather characteristic sparticle spectroscopy, which can be tested at the LHC. We highlight a few benchmark points in which the lightest neutralino saturates the WMAP bound on cold dark matter abundance.

In orbifold models, gauge, Higgs, and the matter fields can be unified in one multiplet from the compactification of higher dimensional supersymmetric gauge theory. We study how three families of chiral fermions can be unified in the gauge multiplet. The bulk gauge interaction includes the Yukawa interactions to generate masses for quarks and leptons after the electroweak symmetry is broken. The bulk Yukawa interaction has global or gauged flavor symmetry originating from the $R$ symmetry or bulk gauge symmetry, and the Yukawa structure is restricted. When the global and gauged flavor symmetries are broken by orbifold compactification, the remaining gauge symmetry which contains the standard model gauge symmetry is restricted. The restrictions from the bulk flavor symmetries can provide explanations of fermion mass hierarchy.

We motivate and explore the possibility that extra $SU(N)$ gauge groups may exist independently of the standard model groups, yet not be subgroups of some grand unified group. We study the running of the coupling constants as potential evidence for a common origin of all the gauge theories. Several different examples are displayed. Some of the multiple options involve physics at the TeV scale.