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We review minimal realistic grand unified models based on $SU(5)$ and $SO(10)$ gauge groups. The models with small Higgs representations and higher dimensional operators - under the assumption of no cancellations in proton decay amplitudes…
We identify a variety of coannihilation scenarios in a supersymmetric SU(4)_c x SU(2)_L x SU(2)_R model with discrete left-right symmetry. Non-universal gaugino masses, compatible with the gauge symmetry, play an essential role in realizing…
We introduce new techniques for calculations in Gauge theories with extended supersymmetry. We are working in Projective Superspace where the $SU(2)$ R-symmetry is realized geometrically by including an auxilliary $\mathbb{CP}^1$ component…
A phenomenological analysis of the three-family local gauge group $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ with right-handed neutrinos is carried out. Instead of using the minimal scalar sector able to break the symmetry in a proper way, we…
There are suggestive experimental indications that the leptons, neutrinos, and quarks are composite and that their structure is described by the quantum group SLq(2). Since the hypothetical preons must be very heavy relative to the masses…
The spontaneous breaking of SU(4) heterotic standard models by Z_3 x Z_3 Wilson lines to the MSSM with three right-handed neutrino supermultiplets and gauge group SU(3)_C x SU(2)_L x U(1) x U(1) is explored. The two-dimensional subspace of…
We provide a world-sheet interpretation to the plane wave limit of a large class of exact supergravity backgrounds in terms of logarithmic conformal field theories. As an illustrative example, we consider the two-dimensional conformal field…
The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the…
In the context of a strongly coupled Electroweak Symmetry Breaking, composite triplet of heavy vectors belonging to the $SU(2)_{L+R}$ adjoint representation and a composite scalar singlet under $SU(2)_{L+R}$ may arise from a new strong…
We discuss the possibility of constructing an effective gauge field theory of the nucleon interations based on the ideas of isotopic invariance as well as hypercharge invariance as a local gauge symmetry and spontaneous breaking of this…
The complete spectrum of states in the supersymmetric principal chiral model based on SU(n) is conjectured, and an exact factorizable S-matrix is proposed to describe scattering amongst these states. The SU(n)_L*SU(n)_R symmetry of the…
We study SU(3)$_L\timesSU(3)_R$ chiral quark model of mesons up to the next to leading order of $1/N_c$ expansion. Composite vector and axial-vector mesons resonances are introduced via non-linear realization of chiral SU(3) and vector…
The apparent absence of new heavy states at the LHC below the TeV scale points that there is a gap in the electroweak energy spectrum. This scenario is conveniently described through the electroweak effective theory, an effective…
A general procedure for the derivation of SU(3)\supset U(2) reduced Wigner coefficients for the coupling (\lambda_{1}\mu_{1})\times (\lambda_{2}\mu_{2})\downarrow (\lambda\mu)^{\eta}, where \eta is the outer multiplicity label needed in the…
We provide a non-linear realisation of composite Higgs models in the context of the SU(4)/Sp(4) symmetry breaking pattern, where the effective Lagrangian of the spin-0 and spin-1 resonances is constructed via the CCWZ prescription using the…
The naturalness problem in the Higgs sector finds a popular solution in composite Higgs models. In such theories the Higgs boson emerges as the pseudo-Nambu-Goldstone boson associated with the breaking of a global symmetry realised in a…
QCD justification of SU(m/n) supergroups are shown to provide a basis for the existence of an approximate hadronic supersymmetry. Effective Hamiltonian of the relativistic quark model is derived, leading to hadronic mass formulae in…
We report on the status of our programme to simulate Sp($2N$) gauge theories on the lattice. Motivated by the potential realization of an SU($4$)/Sp($4$)$\sim$SO($6$)/SO($5$) composite Higgs model and the applications to self interacting…
Rigid body dynamics on the rotation group have typically been represented in terms of rotation matrices, unit quaternions, or local coordinates, such as Euler angles. Due to the coordinate singularities associated with local coordinate…
As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) $\to$ Sp(4) global symmetry breaking…