On Generalized Self-Duality Equations Towards Supersymmetric Quantum Field Theories Of Forms

We classify possible `self-duality' equations for p-form gauge fields in space-time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T invariant under a sub-group H of SO(D). Second, the representation for the SO(D) curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the `self-duality' equations can be candidates as gauge functions for SO(D)-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for dimensions greater than 9, for various p-form gauge fields.Comment: 20 pages, Late

Solving Gauge Invariant Systems without Gauge Fixing: the Physical Projector in 0+1 Dimensional Theories

The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require gauge fixing nor any additional degrees of freedom beyond the original ones---two characteristic features of all other available methods for quantising constrained dynamics---is put to work in the context of a general class of quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge groups are considered specifically, and a comprehensive understanding of the corresponding physical spectra is achieved in a straightforward manner, using only standard methods of coherent states and group theory which are directly amenable to generalisation to other Lie algebras. Results extend by far the few examples available in the literature from much more subtle and delicate analyses implying gauge fixing and the characterization of modular space.Comment: 32 pages, LaTeX fil

Mersenne Primes, Polygonal Anomalies and String Theory Classification

It is pointed out that the Mersenne primes $M_p=(2^p-1)$ and associated perfect numbers ${\cal M}_p=2^{p-1}M_p$ play a significant role in string theory; this observation may suggest a classification of consistent string theories.Comment: 10 pages LaTe

See-Saw Masses for Quarks and Leptons in SU(5)

We build on a recent paper by Grinstein, Redi and Villadoro, where a see-saw like mechanism for quark masses was derived in the context of spontaneously broken gauged flavour symmetries. The see-saw mechanism is induced by heavy Dirac fermions which are added to the Standard Model spectrum in order to render the flavour symmetries anomaly-free. In this letter we report on the embedding of these fermions into multiplets of an SU(5) grand unified theory and discuss a number of interesting consequences.Comment: 15 pages, 4 figures (v3: outline restructured, modified mechanism to cancel anomalies

Symmetry Scheme for Amino Acid Codons

Group theoretical concepts are invoked in a specific model to explain how only twenty amino acids occur in nature out of a possible sixty four. The methods we use enable us to justify the occurrence of the recently discovered twenty first amino acid selenocysteine, and also enables us to predict the possible existence of two more, as yet undiscovered amino acids.Comment: 18 pages which include 4 figures & 3 table

Bounds on neutrino masses from leptogenesis in type-II see-saw models

The presence of the triplet $\Delta_{L}$ in left-right symmetric theories leads to type-II see-saw mechanism for the neutrino masses. In these models, assuming a normal mass hierarchy for the heavy Majorana neutrinos, we derive a lower bound on the mass of the lightest of heavy Majorana neutrino from the leptogenesis constraint. From this bound we establish a consistent picture for the hierarchy of heavy Majorana neutrinos in a class of left right symmetric models in which we identify the neutrino Dirac mass matrix with that of Fritzsch type charged lepton mass matrix. It is shown that these values are compatible with the current neutrino oscillation data.Comment: minor typos corrected, references added, match with published versio

Implications of LEP Results for SO(10) Grandunification with Two Intermediate Stages

We consider the breaking of the grand unification group $SO(10)$ to the standard model gauge group through several chains containing two intermediate stages. Using the values of the gauge coupling constants at scale $M_Z$ derived from recent LEP data, we determine the range of their intermediate and unification scales. In particular, we identify those chains that permit new gauge structure at relatively low energy $(\sim 1\, {\rm TeV})$.Comment: (LATEX, 9 pages + 3 pages of figures not included) OITS-48

On Composite Two Higgs Doublet Models

We investigate composite two Higgs doublet models realized as pseudo Goldstone modes, generated through the spontaneous breaking of a global symmetry due to strong dynamic at the TeV scale. A detailed comparative survey of two possible symmetry breaking patterns, SU(5) -> SU(4) x U(1) and SU(5) x SU(4), is made. We point out choices for the Standard Model fermion representations that can alleviate some phenomenological constraints, with emphasis towards a simultaneous solution of anomalous Zb\bar{b} coupling and Higgs mediated Flavor Changing Neutral Currents. We also write down the kinetic lagrangian for several models leading to Two Higgs Doublets and identify the anomalous contributions to the T parameter. Moreover, we describe a model based on the breaking $SO(9)/SO(8)$ in which there is no tree-level breaking of custodial symmetry, discussing also the possible embeddings for the fermion fields.Comment: 17 pages. Mistake corrected, added one section on a T- and flavor safe model based on SO(9)/SO(8). Matches published versio

Triplet Leptogenesis in Left-Right Symmetric Seesaw Models

We discuss scalar triplet leptogenesis in a specific left-right symmetric seesaw model. We show that the Majorana phases that are present in the model can be effectively used to saturate the existing upper limit on the CP-asymmetry of the triplets. We solve the relevant Boltzmann equations and analyze the viability of triplet leptogenesis. It is known for this kind of scenario that the efficiency of leptogenesis is maximal if there exists a hierarchy between the branching ratios of the triplet decays into leptons and Higgs particles. We show that triplet leptogenesis typically favors branching ratios with not too strong hierarchies, since maximal efficiency can only be obtained at the expense of suppressed CP-asymmetries.Comment: 16 pages, 5 figures, published versio

Possible Candidates for SUSY SO(10) Model with an Intermediate Scale

We study the possibility of an intermediate scale existing in supersymmetric SO(10) grand unified theories: The intermediate scale is demanded to be around 10^{12} GeV so that neutrinos can obtain masses suitable for explaining the experimental data on the deficit of solar neutrino with Mikheev-Smirnov-Wolfenstein solution and the existence of hot dark matter. We show that any Pati-Salam type intermediate symmetries are excluded by requiring reasonable conditions and only $SU(2)_L\times SU(2)_R \times SU(3)_C\times U(1)_{B-L}$ is likely to be realized as an intermediate symmetry.Comment: LaTeX, 8 pages + 1 uuencoded eps figure (Error corrected