SL(2,C)-gauge theory,N=1 supergravity and torsion
It is shown that the SL(2,C)-gauge theory of gravitation may be considered to correspond toN = 1 supergravity and the conserved current gives rise to the Einstein-Cartan action. The torsion term here appears due to the spinorial variableθ, which is associated with the “internal helicity” giving rise to the isospin algebra from the conformal reflection group. In this sense, the internal symmetry of hadrons is found to take a dominant role in gravitational phenomena in the microlocal space-time region where the Einstein-Cartan action becomes significant.

title: EXTENDED CONFORMAL GROUP, SUPERSYMMETRY, AND GEOMETRICAL PROPERTIES OF HADRONS
abstract: We have studied the interrelation among conformal symmetry, internal symmetry and super-symmetry and have shown that extended conformal group which includes, apart from conformal transformation, space, time and conformal reflection can give rise to internal symmetry algebra as well as supersymmetry algebra. To achieve this result, we have dealt with conformal spinors which are taken to be the constituents of the hadrons and these split into two Cartan semispinors or Dirac spinors in the Minkowski space, giving rise to the particle and antiparticle configurations. Supersymmetry is broken here just by the mass term and as such no massless hadron can exist in nature. The internal symmetry arises from the discrete symmetry of reflection. The most significant feature of this formalism is that the symmetry structure helps us to explain the meson-baryon mass difference in an elegant way and the role of fictitious superpartners is completely avoided. Again, any baryon number nonconserving process like proton decay is found to be forbidden by the Lorentz invariance. Finally, it is noted that though the discrete symmetry of reflection is taken to be the origin of the internal symmetry, topological nontrivial structures like strings do not appear here and this also avoids the possibility of the nonconservation of global charge.

title: QUANTUM HALL SKYRMIONS IN THE FRAMEWORK OF O(4) NONLINEAR SIGMA MODEL
abstract: A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these skyrmions.

title: EQUIVALENCE OF STOCHASTIC, KLAUDER AND GEOMETRIC QUANTIZATION
abstract: The relativistic generalization of stochastic quantization helps us to introduce a stochastic-phase-space formulation when a relativistic quantum particle appears as a stochastically extended one. The nonrelativistic quantum mechanics is obtained in the sharp point limit. This also helps us to introduce a gauge-theoretical extension of a relativistic quantum particle when for a fermion the group structure of the gauge field is SU(2). The sharp point limit is obtained when we have a minimal contribution of the residual gauge field retained in the limiting procedure. This is shown to be equivalent to the geometrical approach to the phase-space quantization introduced by Klauder if it is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher-dimensional configuration space when quantization corresponds to freezing the particle to its first Landau level. The geometric quantization then appears as a natural consequence of these two formalisms, since the Hermitian line bundle introduced there finds a physical meaning in terms of the inherent gauge field in stochastic-phase-space formulation or in the interaction with the magnetic field in Klauder quantization.

title: Stochastic field theory at finite temperature, supersymmetry, and witten index
abstract: Finite temperature supersymmetry is studied here from the point of view of stochastic field theory and the formalism of thermofield dynamics. It is shown that the Witten index can take only the values 1 and ½ in this formalism. It is pointed out that when at a critical temperature T c , below which supersymmetry is spontaneously broken, the zero energy mode is given by a thermal doublet of opposite statistics when the index is 1. However, when the index is ½, the zero energy mode is given by a thermal doublet of the same fermionic statistics.

title: Random fields, ising model and bosson-fermion phase transition
abstract: SummaryIt is here shown that when the stochastic quantization procedure is introduced to a massive Thirring fermion where the latter is described as a bound state of massless oscillators interacting through a gradient term in a linear chain, we find that a boson-fermion phase transition occurs at a critical temperatureT =Tc, and atT >Tc supersymmetry is restored. In this scheme supersymmetry is broken by the generation of mass which arises due to the presence of the gradient term.

title: Probing non-universal gaugino masses via Higgs boson production under SUSY cascades at the LHC: a detailed study
abstract: Cascade decays of Supersymmetric (SUSY) particles are likely to be prolific sources of Higgs bosons at the Large Hadron Collider (LHC). In this work, we explore, with the help of detailed simulation, the role of non-universal gaugino masses in the production of the Higgs bosons under SUSY cascades. The analysis is carried out by choosing an appropriate set of benchmark points with non-universal gaugino masses in the relevant SUSY parameter space and then contrasting the resulting observations with the corresponding cases having universal relationship among the same. It is shown that even of data at an early phase of the LHC-run with 10 fb−1 one would be able to see, under favourable situations, the imprint of non-universal gaugino masses by reconstructing various Higgs boson resonances and comparing their rates. With increased accumulated luminosities, the indications would naturally become distinct over a larger region of the parameter space.

title: Probing Higgs bosons via the type III seesaw mechanism at the LHC
abstract: We show that the type III seesaw mechanism opens up a promising possibility of searching the Higgs boson in the $b \bar b$ channel through the Higgs production associated with a charged lepton coming from the decay of the triplet seesaw particle. In particular we look for the $2b$ signals with trileptons or same-sign dileptons to construct the Higgs and the triplet fermion mass and calculate the reach with the integrated luminosity of 10 fb$^{-1}$ at the 14 TeV LHC.

title: Higgs signatures in inverse seesaw model at the LHC
abstract: A bstractIn the inverse seesaw mechanism where the spontaneously broken B-L symmetry induces tiny B-L violating Majorana masses for right-handed neutrinos, non-standard Higgs signatures can arise due to a possible Higgs doublet and singlet mixing and/or Higgs boson decays to a left- and right-handed neutrino. This leads to a remarkable feature of hadronically quiet di-lepton final states which can exhibit, in particular, lepton flavour violating signatures coming from flavour-dependent neutrino Yukawa couplings. In this process, one lepton coming from the right-handed decay could be soft enough can be missed by the trigger level cuts of CMS and ATLAS for the di-lepton plus missing energy signature. The prospects of such a signature are investigated for 8 TeV and 14 TeV center of mass energy of the LHC, taking the maximum value of the allowed neutrino Yukawa coupling and the right-handed neutrino mass of 100 GeV. A PYTHIA level simulation shows that the integrated luminosity of 10-20/fb and 1.6/fb for 8 TeV is required to observe the inclusive leptonic and lepton flavour violating signatures, respectively. For 14 TeV, the reach is more and a larger parameter space of the inverse seesaw model can be probed.

title: Boosted top quarks in supersymmetric cascade decays at the LHC
abstract: At the LHC, a generic supersymmetric cascade can be a source of top quark. Specifically third generation squarks and gluino are the major sources of top quark which could also be boosted. In this article, we have shown that jet substructure algorithm can be very useful in identifying such boosted top quarks in the cascade. We take inclusive three jets plus zero lepton plus missing energy final state and try to reconstruct at least one hadronically decaying top quark by using top tagging techniques which has good prospect at the LHC.

title: Signatures of gaugino mass non-universality in cascade Higgs production at the LHC
abstract: Supersymmetric cascades, involving charginos and neutralinos at various stages, contribute in a significant way to Higgs production at the LHC. We explore the nature of such cascades, completely relaxing the universality of the gaugino masses. It is found that the deviation from the scenario with universal gaugino masses would be reflected in the relative production rates for the lightest neutral Higgs and the charged Higgses.