Bosonic Generators Research Articles

Resonant superalgebras for supergravity

Considering supergravity theory is a natural step in the development of gravity models. This paper follows the “algebraic“ path and constructs possible extensions of the Poincaré and Anti-de-Sitter algebras, which inherit their basic commutation structure. Previously achieved results of this type are fragmentary and show only a limited fraction of possible algebraic realizations. Our paper presents the newly obtained symmetry algebras, evaluated within an efficient pattern-based computational method of generating the so-called ‘resonating’ algebraic structures. These supersymmetric extensions of algebras, going beyond the Poincaré and Anti-de Sitter ones, contain additional bosonic generators Z_{ab} (Lorentz-like), and U_a (translational-like) added to the standard Lorentz generator J_{ab} and translation generator P_{a}. Our analysis includes all cases up to two fermionic supercharges, Q_{alpha } and Y_{alpha }. The delivered plethora of superalgebras includes few past results and offers a vastness of new examples. The list of the cases is complete and contains all superalgebras up to two of Lorentz-like, translation-like, and supercharge-like generators (JP+Q)+(ZU+Y)=JPZU+QY. In the latter class, among 667 founded superalgebras, the 264 are suitable for direct supergravity construction. For each of them, one can construct a unique supergravity model defined by the Lagrangian. As an example, we consider one of the algebra configurations and provide its Lagrangian realization.

Gauging the superconformal group with a graded dual operator

Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator allows us to construct an action that is gauge invariant under the grading even bosonic generators. We provide a self-dual notion based on the dual operator. We use the definition of the dual operator to contruct a model with gauge invariance SO(1, 3) × SU(N) × U(1) ⊂ SU(2, 2|N). The choice of a graded dual operator allows us to overcome technical difficulties of U(N) unified theories based on the superconformal group. The gravity action reproduces the Einstein-Hilbert action in certain sector of the theory. The definition of the dual operator allows us to include fermionic matter in the gauge connection in a geometric manner. We give a summary with possible phenomenological parameters that are included in the model.

Warped AdS2 and SU(1, 1|4) symmetry in Type IIB

We investigate the existence of solutions with 16 supersymmetries to Type IIB supergravity on a spacetime of the form AdS2× S5× S1 warped over a two-dimensional Riemann surface Σ. The existence of the Lie superalgebra SU(1, 1|4) ⊂ PSU(2, 2|4), whose maximal bosonic subalgebra is SO(1, 2)⊕SO(6)⊕SO(2), motivates the search for half-BPS solutions with this isometry that are asymptotic to AdS5×S5. We reduce the BPS equations to the Ansatz for the bosonic fields and supersymmetry generators compatible with these symmetries, then show that the only non-trivial solution is the maximally supersymmetric solution AdS5× S5. We argue that this implies that no solutions exist for fully back-reacted D7 probe or D7/D3 intersecting branes whose near-horizon limit is of the form AdS2× S5× S1× Σ.

Resonant superalgebras and [formula omitted] supergravity theories in three spacetime dimensions

We explore N=1 supersymmetric extensions of algebras going beyond the Poincaré and AdS ones in three spacetime dimensions. Besides reproducing two known examples, we present new superalgebras, which all correspond to supersymmetric extensions with one fermionic charge Qα concerning the so-called resonant algebras being characterized by the presence of an additional bosonic generator Za. We point out particular requirements that superalgebras have to satisfy to be successfully incorporated within valid supergravity actions. The presented algebraic and Lagrangian framework helps us better understand the relations between the various supergravity and supersymmetric Chern-Simons actions invariant under diverse resonant superalgebras.

Three-dimensional Maxwellian extended Bargmann supergravity

We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the non-relativistic limits of the minimal and the mathcal{N} = 2 Maxwell superalgebras. We show that a well-defined Maxwellian extended Bargmann supergravity requires to construct by hand a supersymmetric extension of the Maxwellian extended Bargmann algebra by introducing additional fermionic and bosonic generators. The new non-relativistic supergravity action presented here contains the extended Bargmann supergravity as a sub-case.

Sp(4, R) algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry

In this paper we introduce the bosonic generators of the $sp(4,R)$ algebra and study some of their properties, based on the $SU(1,1)$ and $SU(2)$ group theory. With the developed theory of the $Sp(4,R)$ group, we solve the interaction part of the most general Hamiltonian of a two-level system in two-dimensional geometry in an exact way. As particular cases of this Hamiltonian, we reproduce the solution of earlier problems as the Dirac oscillator and the Jaynes-Cummings model with one and two modes of oscillation.

Local \u03b2-deformations and Yang-Baxter sigma model

Homogeneous Yang-Baxter (YB) deformation of AdS5 × S5 superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to β-deformations of the AdS5 ×S5 background when the classical r-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10, 10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing H-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study β-deformations of H-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.

AdS2 \xd7 S6 versus AdS6 \xd7 S2 in Type IIB supergravity

We obtain the complete local solutions with 16 supersymmetries to Type IIB supergravity on a space-time of the form AdS2 × S6 warped over a Riemann surface Σ in terms of two locally holmorphic functions on Σ. We construct the general Ansatz for the bosonic supergravity fields and supersymmetry generators compatible with the SO(2, 1) ⊕ SO(7) isometry algebra of space-time, which extends to the corresponding real form of the exceptional Lie superalgebra F (4). We reduce the BPS equations to this Ansatz, obtain their general local solutions, and show that these local solutions solve the full Type IIB supergravity field equations and Bianchi identities. We contrast the AdS2 × S6 solution with the closely related AdS6 × S2 case and present our results for both in parallel. Finally, we present a preliminary analysis of positivity and regularity conditions for AdS2 × S6, but postpone the construction of globally regular solutions to a subsequent paper.

Perfectly invisible mathcal{P}mathcal{T} -symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry

We investigate a special class of the mathcal{P}mathcal{T} -symmetric quantum models being perfectly invisible zero-gap systems with a unique bound state at the very edge of continuous spectrum of scattering states. The family includes the mathcal{P}mathcal{T} -regularized two particle Calogero systems (conformal quantum mechanics models of de Alfaro-Fubini-Furlan) and their rational extensions whose potentials satisfy equations of the KdV hierarchy and exhibit, particularly, a behaviour typical for extreme waves. We show that the two simplest Hamiltonians from the Calogero subfamily determine the fluctuation spectra around the mathcal{P}mathcal{T} -regularized kinks arising as traveling waves in the field-theoretical Liouville and SU(3) conformal Toda systems. Peculiar properties of the quantum systems are reflected in the associated exotic nonlinear supersymmetry in the unbroken or partially broken phases. The conventional mathcal{N}=2 supersymmetry is extended here to the mathcal{N}=4 nonlinear supersymmetry that involves two bosonic generators composed from Lax-Novikov integrals of the subsystems, one of which is the central charge of the superalgebra. Jordan states are shown to play an essential role in the construction.

P-Brane superalgebras via integrability

It has long been appreciated that superalgebras with bosonic and fermionic generators additional to those in the super-Poincare algebra underlie p-brane and D-brane actions in superstring theory. These algebras have been revealed via “bottom up” approaches, involving consideration of Noether charges, and by “top down” approaches, involving the construction of manifestly supersymmetry invariant Wess–Zumino actions. In this paper, we give an alternative derivation of these algebras based on integrability of supersymmetry transformations assigned to fields in order to solve a cohomology problem related to the construction of Wess–Zumino terms for p-brane and D-brane actions.

On the Distinction between Debye Bosons and Phonons

A method is described that allows one to construct the dispersion of the Debye bosons (sound waves) from the known temperature dependence of the sound velocities. The method simply assumes that the sound velocity measured at temperature T gives the slope of the dispersion relation at excitation energy E=kB·T. The associated reduced wave vector is set equal to q/q0=a0kBT/hvL/T. In this way the dispersion of the Debye bosons can be constructed for all thermal energies for which sound velocities vL/T(T) are known. This can be up to melting temperature. Surprisingly, the dispersion of the Debye bosons continues beyond zone boundary. At melting temperature the wavelength of the Debye bosons is of the order of the atomic diameters. The sources of the Debye bosons therefore must have atomic dimensions. Spontaneous generation of Debye bosons by individual atoms is, however, a completely unexplored process. Interactions with the atomistic background of phonons or lattice defects provide damping to the Debye bosons and make vL/T(T) sample and temperature dependent. Quite generally vL/T(T) decreases as a function of increasing temperature. For high energies the dispersion relation of the Debye bosons therefore becomes visibly lower than linear. Interactions between Debye bosons and phonons can modify the dispersion of the acoustic phonons appreciably. Because of their different symmetries the dispersion relations of Debye bosons and acoustic phonons attract each other. It is observed that for low wave vector values the dispersion of the acoustic phonons can assume the linear wave vector dependence of the Debye bosons. At the end of the linear section a functional crossover to a sine-like function of wave vector occurs.

Hypersymmetry bounds and three-dimensional higher-spin black holes

We investigate the hypersymmetry bounds on the higher spin black hole parameters that follow from the asymptotic symmetry superalgebra in higher-spin anti-de Sitter gravity in three spacetime dimensions. We consider anti-de Sitter hypergravity for which the analysis is most transparent. This is a $osp(1\vert 4) \oplus osp(1\vert 4)$ Chern-Simons theory which contains, besides a spin-$2$ field, a spin-$4$ field and a spin-$5/2$ field. The asymptotic symmetry superalgebra is then the direct sum of two-copies of the hypersymmetric extension $W_{(2,\frac52,4)}$ of $W_{(2,4)}$, which contains fermionic generators of conformal weight $5/2$ and bosonic generators of conformal weight $4$ in addition to the Virasoro generators. Following standard methods, we derive bounds on the conserved charges from the anticommutator of the hypersymmetry generators. The hypersymmetry bounds are nonlinear and are saturated by the hypersymmetric black holes, which turn out to possess $1/4$-hypersymmetry and to be "extreme", where extremality can be defined in terms of the entropy: extreme black holes are those that fulfill the extremality bounds beyond which the entropy ceases to be a real function of the black hole parameters. We also extend the analysis to other $sp(4)$-solitonic solutions which are maximally (hyper)symmetric.

Prediction and Derivation of the Hubble Constant from Subatomic Data Utilizing the Harmonic Neutron Hypothesis

Purpose: To accurately derive H0 from subatomic constants in abscence of any standard astronomy data. Methods: Recent astronomical data have determined a value of Hubble’s constant to range from 76.9+3.9-3.4+10.0-8.0 to 67.80 ± 0.77 (km/s)/Mpc. An innovative prediction of H0 is obtained from harmonic properties of the frequency equivalents of neutron, n0, in conjunction with the electron, e; the Bohr radius, α0; and the Rydberg constant, R. These represent integer natural unit sets. The neutron is converted from its frequency equivalent to a dimensionless constant,, where “h” = Planck’s constant, and “s” is measured in seconds. The fundamental frequency, Vf, is the first integer series set . All other atomic data are scaled to Vf as elements in a large, but a countable point set. The present value of H0 is derived and ΩM assumed to be 0. An accurate derivation of H0 is made using a unified power law. The integer set of the first twelve integers N12 {1,2,…,11,12}, and their harmonic fractions exponents of Vf represent the first generation of bosons and particles. Thepartial harmonic fraction, -3/4, is exponent of Vf which represents H0. The partial fraction 3/4 is associated with a component of neutron beta decay kinetic energy. Results: H0 is predicted utilizing a previously published line used to derive Planck time, tp. The power law line of the experimental H0 and tp conforms to the predicted line. Conclusions: H0 can be predicted from subatomic data related to the neutron and hydrogen.

Generation of Pseudoscalar Bosons by Stimulated Raman Scattering of Light in Dielectric Media

The conditions of pseudoscalar excitations of liquids and crystals vibration states in spontaneous and stimulated Raman spectra revealing are reported. The selection rules for pseudoscalar modes of molecules and crystals observation have been obtained. The experiments on observation of spontaneous and stimulated Raman scattering on pseudoscalar modes of molecules and crystals have been fulfilled. The excitation of stimulated Raman scattering was with using of solid state laser YAG:Nd3+ , generating intense (up to 1 TW/cm2) ultrashort (60 ps) laser pulses with energy 10 mJ and frequency repetition 10 Hz. The relationship between pseudoscalar bosons of dielectric media and axion of vacuum is analyzed.

Soliton defects in one-gap periodic system and exotic supersymmetry

By applying Darboux--Crum transformations to the quantum one-gap Lam\'e system, we introduce an arbitrary countable number of bound states into forbidden bands. The perturbed potentials are reflectionless and contain two types of soliton defects in the periodic background. The bound states with a finite number of nodes are supported in the lower forbidden band by the periodicity defects of the potential well type, while the pulse-type bound states in the gap have an infinite number of nodes and are trapped by defects of the compression modulations nature. We investigate the exotic nonlinear $\mathcal{N}=4$ supersymmetric structure in such paired Schr\"odinger systems, which extends an ordinary $\mathcal{N}=2$ supersymmetry and involves two bosonic generators composed from Lax--Novikov integrals of the subsystems. One of the bosonic integrals has a nature of a central charge and allows us to liaise the obtained systems with the stationary equations of the Korteweg--de Vries and modified Korteweg--de Vries hierarchies. This exotic supersymmetry opens the way for the construction of self-consistent condensates based on the Bogoliubov--de Gennes equations and associated with them new solutions to the Gross--Neveu model. They correspond to the kink or kink-antikink defects of the crystalline background in dependence on whether the exotic supersymmetry is unbroken or spontaneously broken.

Twisted superalgebras and cohomologies of the [formula omitted] superconformal quantum mechanics

We prove that the invariance of the N = 2 superconformal quantum mechanics is controlled by subalgebras of a given twisted superalgebra made of 6 fermionic (nilpotent) generators and 6 bosonic generators (including a central charge). The superconformal quantum mechanics actions are invariant under this quite large twisted superalgebra. On the other hand, they are fully determined by a subalgebra with only 2 fermionic and 2 bosonic (the central charge and the ghost number) generators. The invariant actions are Q i -exact ( i = 1 , 2 , … , 6 ), with a Q i ′ -exact ( i ′ ≠ i ) antecedent for all 6 fermionic generators. It follows that the superconformal quantum mechanics actions with Calogero potentials are uniquely determined even if, in its bosonic sector, the twisted superalgebra does not contain the one-dimensional conformal algebra sl ( 2 ) , but only its Borel subalgebra. The general coordinate covariance of the non-linear sigma-model for the N = 2 supersymmetric quantum mechanics in a curved target-space is fully implied only by its worldline invariance under a pair of the 6 twisted supersymmetries. The transformation connecting the ordinary and twisted formulations of the N = 2 superconformal quantum mechanics is explicitly presented.

Supersymmetry algebra cohomology. I. Definition and general structure

This paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra cohomology, and corresponding “primitive elements” are defined by means of a BRST (Becchi-Rouet-Stora-Tyutin)-type coboundary operator. A method to systematically compute this cohomology is outlined and illustrated by simple examples.

Higgs Particle: The Origin of Mass

The Higgs particle is a new elementary particle predicted in the Standard Model of the elementary particle physics. It plays a special role in the theory of mass generation of quarks, leptons, and gauge bosons. In this article, theoretical issues on the Higgs mechanism are first discussed, and then experimental prospects on the Higgs particle study at the future collider experiments, LHC and ILC, are reviewed. The Higgs coupling determination is an essential step to establish the mass generation mechanism, which could lead to a deeper understanding of particle physics.

Landau-Ginzburg realization of open string TFT

We investigate B-type topological Landau-Ginzburg theory with one variable, with D2-brane boundary conditions. We find that the allowed brane configurations are determined in terms of the possible factorizations of the superpotential, and compute the corresponding open string chiral rings. These are characterized by bosonic and fermionic generators that satisfy certain relations. Moreover we show that the disk correlators, being continuous functions of deformation parameters, satisfy the topological sewing constraints, thereby proving consistency of the theory. In addition we show that the open string LG model is, in its content, equivalent to a certain triangulated category introduced by Kontsevich, and thus may be viewed as a concrete physical realization of it.

Differential geometry of the quantum 3-dimensional space

We present a differential calculus on the extension of the quantum plane obtained considering that the (bosonic) generator $x$ is invertible and furthermore working polynomials in $\ln x$ instead of polynomials in $x$. We call quantum Lie algebra to this extension and we obtain its Hopf algebra structure and its dual Hopf algebra. Differential geometry of the quantum Lie algebra of the extended quantum plane and its Hopf algebra structure is obtained. Its dual Hopf algebra is also given.