Tensorial Central Charges Research Articles

Spinor Moving Frame, Polarized Scattering Equation for 11D Supergravity, and Ambitwistor Superstring

We reveal and discuss the spinor moving frame origin of the formalism of the 11D polarized scattering equation by Geyer and Mason [21]. In particular, we use the spinor moving frame formulation of the 11D ambitwistor superstring [35] considered as a dynamical system in the 11D superspace enlarged by tensorial central charge coordinates to rigorously obtain the expression for the spinor function on a Riemann sphere and the polarized scattering equation which that obeys.

On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring

We revisited the formalism of 110 polarized scattering equation by Geyer and Mason from the perspective of spinor frame approach and spinor moving frame formulation of the 110 ambitwistor superstring action. In particular, we rigorously obtain the equation for the spinor function on Riemann sphere from the supertwistor form of the ambitwistor superstring action, write its general solution and use it to derive the polarized scattering equation. We show that the expression used by Geyer and Mason to motivate their ansatz for the solution of polarized scattering equation can be obtained from our solution after a suitable gauge fixing. To this end we use the hidden gauge symmetries of the 110 ambitwistor superstring, including S0(16), and the description of ambitwistor superstring as a dynamical system in an 110 superspace enlarged by bosonic directions parametrized by 517 tensorial central charge coordinates {Z}^{underline{mu}underline {nu }} and {Z}^{underline{mu}underline {nu}underline{rho}underline {sigma}underline{kappa}} . We have also found the fermionic superpartner of the polarized scattering equation. This happens to be a differential equation in fermionic variables imposed on the super­ amplitude, rather then just a condition on the scattering data as the bosonic polarized scattering equation is. D=10 case is also discussed stressing the similarities and differences with 110 systems. The useful formulation of 100 ambitwistor superstring considers it as a dynamical system in superspace enlarged with 126 tensorial central charge coordinates Zμνρσκ.

Quaternionic (super) twistors extensions and general superspaces

In a attempt to treat a supergravity as a tensor representation, the four-dimensional [Formula: see text]-extended quaternionic superspaces are constructed from the (diffeomorphyc) graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors [D. J. Cirilo-Lombardo and V. N. Pervushin, Int. J. Geom. Methods Mod. Phys., doi: http://dx.doi.org/10.1142/S0219887816501139.], with [Formula: see text] These quaternionic superspaces have [Formula: see text] even-quaternionic coordinates and [Formula: see text] odd-quaternionic coordinates, where each coordinate is a quaternion composed by four [Formula: see text]-fields (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case, the number of fields of the supergravity is determined by the number of components of the tensor representation of the four-dimensional [Formula: see text]-extended quaternionic superspaces. The role of tensorial central charges for any [Formula: see text] even [Formula: see text] is elucidated from this theoretical context.

Representations and particles of orthosymplectic supersymmetry generalization

Orthosymplectic osp(1|2n) supersymmetry (alternative names: Generalized conformal supersymmetry with tensorial central charges, conformal M-algebra, parabose algebra) has been considered as an alternative to d-dimensional conformal superalgebra. Due to mathematical difficulties, even classification of its unitary irreducible representations (UIR’s) have not been entirely accomplished. We give this classification for n = 4 case (corresponding to four dimensional space-time) and then show how the discrete subset of these UIR’s can be constructed in a Clifford algebra variation of the Green’s ansatz.

Quantum energies and tensorial central charges of confined monopoles

We study different aspects of monopoles in the Higgs phase which are confined by (non-abelian) vortices in \cal{N}=2 SQCD with gauge group U(N) and N_f >= N massive flavors, including generalized FI-terms. We compute in particular the perturbative quantum corrections for (multiple) confined monopoles and identify an anomalous contribution in the central charge. For N_f = N the results match the quantum corrections for kinks in two-dimensional CP^{N-1} models. To regulate the theory we embedded it in a six-dimensional model with constant U(1) background fields which generate the masses upon dimensional reduction. We discuss the (local) susy algebra and its representations including tensorial central charges, which are carried by the confined monopoles, in an SU(2)_R covariant way. The resulting SU(2)_R covariant 1/4 BPS equations show that there is no correlation between the SU(2)_R and the spatial orientation of the confined monopole system. However, at the quantum level we find that supersymmetry links the spatial SU(2) with the R-symmetry SU(2)_R.

An infinite supermultiplet of massive higher-spin fields

The representation theory underlying the infinite-component relativistic wave equation written by Majorana is revisited from a modern perspective. On the one hand, the massless solutions of this equation are shown to form a supermultiplet of the superPoincare algebra with tensorial central charges; it can also be obtained as the infinite spin limit of massive solutions. On the other hand, the Majorana equation is generalized for any space-time dimension and for arbitrary Regge trajectories. Inspired from these results, an infinite supermultiplet of massive fields of all spins and of equal mass is constructed in four dimensions and proved to carry an irreducible representation of the orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial charges.

Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields

We propose a (3+1)D linear set of covariant vector equations, which unify the spin-0 'new Dirac equation' with its spin-1/2 counterpart, proposed by Staunton. Our equations describe a spin-(0,1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin degrees of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.

Domain walls, the extended superconformal algebra and the supercurrent

The presence of a domain wall is shown to require a tensorial central charge extension of the superconformal algebra. The currents associated with the conformal central charges are constructed as space–time moments of the SUSY tensorial central charge current. The supercurrent is obtained and it contains the R symmetry current, the SUSY spinor currents, the energy–momentum tensor and the SUSY tensorial central charge currents as its component currents. All tensorial central charge extended superconformal currents are constructed from the supercurrent. The superconformal currents' and the conformal tensorial central charge currents' (non-)conservation equations are expressed in terms of the generalized trace of the supercurrent. It is argued that although the SUSY tensorial central charges are uncorrected, the conformal tensorial central charges receive radiative corrections.

Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained generalized supersymmetries admit a dual formulation. For both real and complex spinors generalized supersymmetries are constructed and classified as dimensional reductions of supersymmetries from {\em oxidized} space-times (i.e. the maximal space-times associated to $n$-component Clifford irreps). We apply these results to sistematically construct a class of models describing superparticles in presence of bosonic tensorial central charges, deriving the consistency conditions for the existence of the action, as well as the constrained equations of motion. Examples of these models (which, in their twistorial formulation, describe towers of higher-spin particles) were first introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and Lukierski (for complex spinors).

The symmetry algebras of Euclidean M-theory

We study the Euclidean supersymmetric D=11 M-algebras. We consider two such D=11 superalgebras: the first one is N=(1,1) self-conjugate complex-Hermitean, with 32 complex supercharges and 1024 real bosonic charges, the second is N=(1,0) complex-holomorphic, with 32 complex supercharges and 528 bosonic charges, which can be obtained by analytic continuation of known Minkowski M-algebra. Due to the Bott's periodicity, we study at first the generic D=3 Euclidean supersymmetry case. The role of complex and quaternionic structures for D=3 and D=11 Euclidean supersymmetry is elucidated. We show that the additional 1024−528=496 Euclidean tensorial central charges are related with the quaternionic structure of Euclidean D=11 supercharges, which in complex notation satisfy SU(2) pseudo-Majorana condition. We consider also the corresponding Osterwalder–Schrader conjugations as implying for N=(1,0) case the reality of Euclidean bosonic charges. Finally, we outline some consequences of our results, in particular for D=11 Euclidean supergravity.

BPS preons and tensionless super-p-branes in generalized superspace

Tensionless super-p-branes in a generalized superspace with additional tensorial central charge coordinates may provide an extended object model for BPS preons, i.e., for the hypothetical constituents of M-theory preserving 31 of 32 supersymmetries [I.A. Bandos, J.A. de Azcárraga, J.M. Izquierdo, J. Lukierski, Phys. Rev. Lett. 86 (2001) 4451].

Hamiltonian of Tensionless Strings with Tensor Central Charge Coordinates

A new class of twistor-like string models in four-dimensional space-time extended by the addition of six tensorial central charge (TCC) coordinates $z_{mn}$ is studied. The Hamiltonian of tensionless string in the extended space-time is derived and its symmetries are investigated. We establish that the string constraints reduce the number of independent TCC coordinates $z_{mn}$ to one real effective coordinate which composes an effective 5-dimensional target space together with the $x^{m}$ coordinates. We construct the P.B. algebra of the first class constraints and discover that it coincides with the P.B. algebra of tensionless strings. The Lorentz covariant antisymmetric Dirac $\hat{\mathbf C}$-matrix of the P.B. of the second class constraints is constructed and its algebraic structure is further presented.

Uniform twistor-like formulation of massive and massless superparticles with tensorial central charges

We construct the manifestly Lorentz-invariant twistorial formulation of the N = 1 D = 4 superparticle with tensorial central charges which describes massive and massless cases in a uniform manner. The tensorial central charges are realized in terms of even spinor variables and central charge coordinates. The full analysis of the number of conserved supersymmetries has been carried out. In the massive case the superparticle preserves 1 4 or 1 2 of target-space supersymmetries whereas the massless superparticle preserves two or three supersymmetries.

MASSIVE SUPERPARTICLE WITH TENSORIAL CENTRAL CHARGES

We construct the manifestly Lorenz-invariant formulation of the N = 1, D=4 massive superparticle with tensorial central charges. The model contains a real parameter k and at k≠0 possesses one κ-symmetry while at k=0 the number of κ-symmetry is two. The equivalence of the formulations at all k≠0 is obtained. The local transformations of κ-symmetry are written. It is considered using the index spinor for construction of the tensorial central charges. The equivalence at classical level between the massive D=4 superparticle with one κ-symmetry and the massive D=4 spinning particle is obtained.

1/4 Partial breaking of global supersymmetry and new superparticle actions

We construct the world-line superfield massive superparticle actions which preserve 1/4 portion of the underlying higher-dimensional supersymmetry. The rest of supersymmetry is spontaneously broken and realized by nonlinear transformations. We consider the cases of N=4→N=1 and N=8→N=2 partial breaking. In the first case we present the corresponding Green–Schwarz type target superspace action with one κ-supersymmetry. It is related to the superfield action via a field redefinition. In the second case we find out two possible models, one of which is a direct generalization of the N=4→N=1 case, while another is essentially different. For the first model we formulate Green–Schwarz type action with two κ-supersymmetries. We elaborate on the bosonic part of the superfield action for the second model and find that only in two special limits it takes the standard Nambu–Goto form. In the general case it is determined by a fourth-order algebraic equation. The characteristic common feature of these new superparticle models is that the algebras of their spontaneously broken supersymmetries are non-trivial truncations of the general extensions of N=1 and N=2 Poincaré D=4 superalgebras by tensorial central charges.

More on the tensorial central charges inN=1supersymmetric gauge theories: BPS wall junctions and strings

We study the central extensions of the N=1 superalgebras relevant to the soliton solutions with the axial geometry - strings, wall junctions, etc. A general expression valid in any four-dimensional gauge theory is obtained. We prove that the only gauge theory admitting BPS strings at weak coupling is supersymmetric electrodynamics with the Fayet-Iliopoulos term. The problem of ambiguity of the (1/2,1/2) central charge in the generalized Wess-Zumino models and gauge theories with matter is addressed and solved. A possibility of existence of the BPS strings at strong coupling in N=2 theories is discussed. A representation of different strings within the brane picture is presented.

OSp supergroup manifolds, superparticles, and supertwistors

We construct simple twistor-like actions describing superparticles propagating on a coset superspace $\mathrm{OSp}(1|4)/\mathrm{SO}(1,3)$ (containing the $D=4$ anti--de Sitter space as a bosonic subspace), on a supergroup manifold $\mathrm{OSp}(1|4)$ and, generically, on $\mathrm{OSp}(1|2n).$ Making two different contractions of the superparticle model on the $\mathrm{OSp}(1|4)$ supermanifold we get massless superparticles in Minkowski superspace without and with tensorial central charges. Using a suitable parametrization of $\mathrm{OSp}(1|2n)$ we obtain even $\mathrm{Sp}(2n)$-valued Cartan forms which are quadratic in Grassmann coordinates of $\mathrm{OSp}(1|2n).$ This result may simplify the structure of brane actions in super--anti--de Sitter (AdS) backgrounds. For instance, the twistor-like actions constructed with the use of the even $\mathrm{OSp}(1|2n)$ Cartan forms as supervielbeins are quadratic in fermionic variables. We also show that the free bosonic twistor particle action describes massless particles propagating in arbitrary space-times with a conformally flat metric, in particular, in Minkowski space and AdS space. Applications of these results to the theory of higher spin fields and to superbranes in AdS superbackgrounds are mentioned.

Superparticle models with tensorial central charges

A generalization of the Ferber-Shirafuji formulation of superparticle mechanics is considered. The generalized model describes the dynamics of a superparticle in a superspace extended by tensorial central charge coordinates and commuting twistorlike spinor variables. The $D=4$ model contains a continuous real parameter $a>~0$ and at $a=0$ reduces to the $SU(2,2|1)$ supertwistor Ferber-Shirafuji model, while at $a=1$ one gets an $OSp(1|8)$ supertwistor model proposed by two of the authors which describes BPS states with all but one unbroken target space supersymmetries. When $0<a<1$ the model admits an $OSp(2|8)$ supertwistor description, and when $a>1$ the supertwistor group becomes $OSp(1,1|8).$ We quantize the model and find that its quantum spectrum consists of massless states of an arbitrary (half-)integer helicity. The independent discrete central charge coordinate describes the helicity spectrum. We also outline the generalization of the $a=1$ model to higher space-time dimensions and demonstrate that in $D=3,$ 4, 6, and 10, where the quantum states are massless, the extra degrees of freedom (with respect to that of the standard superparticle) parametrize compact manifolds. These compact manifolds can be associated with higher-dimensional helicity states. In particular, in $D=10$ the additional ``helicity'' manifold is isomorphic to the sphere ${S}^{7}.$

TENSORIAL CENTRAL CHARGES AND NEW SUPERPARTICLE MODELS WITH FUNDAMENTAL SPINOR COORDINATES

We consider firstly simple D=4 superalgebra with six real tensorial central charges Zμν, and discuss its possible realizations in massive and massless cases. Massless case is dynamically realized by generalized Ferber–Shirafuji (FS) model with fundamental bosonic spinor coordinates. The Lorentz invariance is not broken due to the realization of central charges generators in terms of bosonic spinors. The model contains four fermionic coordinates and possesses three κ-symmetries thus providing the BPS configuration preserving 3/4 of the target space supersymmetries. We show that the physical degrees of freedom (eight real bosonic and one real Grassmann variable) of our model can be described by OSp (8|1) supertwistor. The relation with recent superparticle model by Rudychev and Sezgin is pointed out. Finally we propose a higher-dimensional generalization of our model with one real fundamental bosonic spinor. D=10 model describes massless superparticle with composite tensorial central charges and in D=11 we obtain zero-superbrane model with nonvanishing mass which is generated dynamically.