Extensions of the Poincare group

We construct an extension of the Poincare group which involves a mixture of internal and space-time supersymmetries. The resulting group is an extension of the superPoincare group with infinitely many generators which carry internal and space-time indices. It is a closed algebra since all Jacobi identities are satisfied and it has therefore explicit matrix representations. We investigate the massless case and construct the irreducible representations of the extended symmetry. They are divided into two sets, longitudinal and transversal representations. The transversal representations involve an infinite series of integer and half-integer helicities. Finally we suggest an extension of the conformal group along the same line.Comment: 13 pages, LaTex fil

Algebras, Derivations and Integrals

In the context of the integration over algebras introduced in a previous paper, we obtain several results for a particular class of associative algebras with identity. The algebras of this class are called self-conjugated, and they include, for instance, the paragrassmann algebras of order $p$, the quaternionic algebra and the toroidal algebras. We study the relation between derivations and integration, proving a generalization of the standard result for the Riemann integral about the translational invariance of the measure and the vanishing of the integral of a total derivative (for convenient boundary conditions). We consider also the possibility, given the integration over an algebra, to define from it the integral over a subalgebra, in a way similar to the usual integration over manifolds. That is projecting out the submanifold in the integration measure. We prove that this is possible for paragrassmann algebras of order $p$, once we consider them as subalgebras of the algebra of the $(p+1)\times(p+1)$ matrices. We find also that the integration over the subalgebra coincides with the integral defined in the direct way. As a by-product we can define the integration over a one-dimensional Grassmann algebra as a trace over $2\times 2$ matrices.Comment: 23 pages, few typos corrected. Final version to be published in International Journal of Modern Physic

Modeling missing transverse energy in V+jets at CERN LHC

I discuss a method to model the instrumental response of the CMS and ATLAS detectors at high transverse missing energies to dominant standard model V+jets backgrounds, where V is a Z, gamma or W, using multi-jet QCD events. The method is developed for new physics searches in early data at the Large Hadron Collider (LHC) with minimal recourse to simulation.Comment: Replaced with the published versio

Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD

We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an N=2 Kahler sigma model in 2+1D deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall junction configurations, which are 1/4-BPS objects, but nonetheless preserve two supercharges when viewed as kinks on the wall worldvolume.Comment: 35 pages, 3 figures; v2: minor corrections and a reference added, to appear in Phys. Rev.

New Einstein-Hilbert-type Action and Superon-Graviton Model(SGM) of Nature

A nonlinear supersymmetric(NLSUSY) Einstein-Hilbert(EH)-type new action for unity of nature is obtained by performing the Einstein gravity analogue geomtrical arguments in high symmetry spacetime inspired by NLSUSY. The new action is unstable and breaks down spontaneously into E-H action with matter in ordinary Riemann spacetime. All elementary particles except graviton are composed of the fundamental fermion "superon" of Nambu-Goldstone(NG) fermion of NLSUSY and regarded as the eigenstates of SO(10) super-Poincar\'e (SP) algebra, called superon-graviton model(SGM) of nature. Some phenomenological implications for the low energy particle physics and the cosmology are discussed. The linearization of NLSUSY including N=1 SGM action is attempted explicitly to obtain the linear SUSY local field theory, which is equivalent and renormalizable.Comment: 37 pages, Latex, Based on a talk by K. Shima at International Conference on Mathematics and Nucler Physics for the 21st Century, March 8-13, 2003, Atomic Energy Authority, Cairo, Egyp

Exact Results in Gauge Theories: Putting Supersymmetry to Work. The 1999 Sakurai Prize Lecture

Powerful methods based on supersymmetry allow one to find exact solutions to certain problems in strong coupling gauge theories. The inception of some of these methods (holomorphy in the gauge coupling and other chiral parameters, in conjunction with instanton calculations) dates back to the 1980's. I describe the early exact results -- the calculation of the beta function and the gluino condensate -- and their impact on the subsequent developments. A brief discussion of the recent breakthrough discoveries where these results play a role is given.Comment: Based on the talk at the Centennial Meeting of The American Physical Society, March 20-26, Atlanta, GA. LaTex (uses sprocl.sty), 36 pages, 5 eps figures include

Grand Unification as a Bridge Between String Theory and Phenomenology

In the first part of the talk, I explain what empirical evidence points to the need for having an effective grand unification-like symmetry possessing the symmetry SU(4)-color in 4D. If one assumes the premises of a future predictive theory including gravity--be it string/M theory or a reincarnation--this evidence then suggests that such a theory should lead to an effective grand unification-like symmetry as above in 4D, near the string-GUT-scale, rather than the standard model symmetry. Advantages of an effective supersymmetric G(224) = SU(2)$_L \times$ SU(2)$_R \times$ SU(4)$^c$ or SO(10) symmetry in 4D in explaining (i) observed neutrino oscillations, (ii) baryogenesis via leptogenesis, and (iii) certain fermion mass-relations are noted. And certain distinguishing tests of a SUSY G(224) or SO(10)-framework involving CP and flavor violations (as in $\mu \to e\gamma$, $\tau \to\mu\gamma$, edm's of the neutron and the electron) as well as proton decay are briefly mentioned. Recalling some of the successes we have had in our understanding of nature so far, and the current difficulties of string/M theory as regards the large multiplicity of string vacua, some comments are made on the traditional goal of understanding {\em vis a vis} the recently evolved view of landscape and anthropism.Comment: A chart showing some insights gained in the world of the very small and that of the very large is included. A few relevant references are added. Some clarification is made in the last section as regards the question of understanding versus landscape and anthropis

Pre - Inflationary Clues from String Theory ?

"Brane supersymmetry breaking" occurs in String Theory when the only available combinations of D-branes and orientifolds are not mutually BPS and yet do not introduce tree-level tachyon instabilities. It is characterized by the emergence of a steep exponential potential, and thus by the absence of maximally symmetric vacua. The corresponding low-energy supergravity admits intriguing spatially-flat cosmological solutions where a scalar field is forced to climb up toward the steep potential after an initial singularity, and additional milder terms can inject an inflationary phase during the ensuing descent. We show that, in the resulting power spectra of scalar perturbations, an infrared suppression is typically followed by a pre-inflationary peak that reflects the end of the climbing phase and can lie well apart from the approximately scale invariant profile. A first look at WMAP9 raw data shows that, while the chi^2 fits for the low-l CMB angular power spectrum are clearly compatible with an almost scale invariant behavior, they display nonetheless an eye-catching preference for this type of setting within a perturbative string regime.Comment: 34 pages, LaTeX, 16 eps figures. Relative displacement in fig. 14 and some typos corrected, references and acknowledgments updated. To appear in JCA

Quadratic pseudosupersymmetry in two-level systems

Using the intertwining relation we construct a pseudosuperpartner for a (non-Hermitian) Dirac-like Hamiltonian describing a two-level system interacting in the rotating wave approximation with the electric component of an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry generators close a quadratic pseudosuperalgebra. A class of time dependent electric fields for which the equation of motion for a two level system placed in this field can be solved exactly is obtained. New interesting phenomenon is observed. There exists such a time-dependent detuning of the field frequency from the resonance value that the probability to populate the excited level ceases to oscillate and becomes a monotonically growing function of time tending to 3/4. It is shown that near this fixed excitation regime the probability exhibits two kinds of oscillations. The oscillations with a small amplitude and a frequency close to the Rabi frequency (fast oscillations) take place at the background of the ones with a big amplitude and a small frequency (slow oscillations). During the period of slow oscillations the minimal value of the probability to populate the excited level may exceed 1/2 suggesting for an ensemble of such two-level atoms the possibility to acquire the inverse population and exhibit lasing properties.Comment: 5 figure

Cosmology and New Physics

A comparison of the standard models in particle physics and in cosmology demonstrates that they are not compatible, though both are well established. Basics of modern cosmology are briefly reviewed. It is argued that the measurements of the main cosmological parameters are achieved through many independent physical phenomena and this minimizes possible interpretation errors. It is shown that astronomy demands new physics beyond the frameworks of the (minimal) standard model in particle physics. More revolutionary modifications of the basic principles of the theory are also discussed.Comment: 37 pages, 5 figures; lectures presented at 9th International Moscow School of Physics (34th ITEP Winter School