Higher Spin Fields in Siegel Space, Currents and Theta Functions

Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequency solutions of relativistic field equations, i.e. particles and antiparticles. Multidimensional Riemann theta functions are shown to solve massless field equations in the Siegel space. We establish the correspondence between conserved higher-spin currents in four-dimensional Minkowski space and those in the ten-dimensional matrix space. It is shown that global symmetry parameters of the current in the matrix space should be singular to reproduce a nonzero current in Minkowski space. The \D-function integral evolution formulae for 4d massless fields in the Fock-Siegel space are obtained. The generalization of the proposed scheme to higher dimensions and systems of higher ranks is considered.Comment: LaTeX, 38 pages, v.3: clarifications, acknowledgements and references added, typos corrected, v.4: more comments and references added, typos corrected, the version to appear in JHE

Geometric Second Order Field Equations for General Tensor Gauge Fields

Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.Comment: 34 pages, LaTeX. Reference adde

Superfield Theories in Tensorial Superspaces and the Dynamics of Higher Spin Fields

We present the superfield generalization of free higher spin equations in tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n) holonomy as a possible framework for the construction of a non-linear higher spin field theory. Surprisingly enough, we find that the most general solution of the supergravity constraints is given by a class of superconformally flat and OSp(1|n)-related geometries. Because of the conformal symmetry of the supergravity constraints and of the higher spin field equations such geometries turn out to be trivial in the sense that they cannot generate a `minimal' coupling of higher spin fields to their potentials even in curved backgrounds with a non-zero cosmological constant. This suggests that the construction of interacting higher spin theories in this framework might require an extension of the tensorial superspace with additional coordinates such as twistor-like spinor variables which are used to construct the OSp(1|2n) invariant (`preonic') superparticle action in tensorial superspace.Comment: LaTeX, 30 pages, no figures. V2. Discussion on conventional constraints extended, typos corrected, JHEP style, to appear in JHE

Lepton asymmetry and the cosmic QCD transition

We study the influence of lepton asymmetry on the evolution of the early Universe. The lepton asymmetry $l$ is poorly constrained by observations and might be orders of magnitude larger than the baryon asymmetry $b$, $|l|/b \leq 2\times 10^8$. We find that lepton asymmetries that are large compared to the tiny baryon asymmetry, can influence the dynamics of the QCD phase transition significantly. The cosmic trajectory in the $\mu_B-T$ phase diagram of strongly interacting matter becomes a function of lepton (flavour) asymmetry. Large lepton asymmetry could lead to a cosmic QCD phase transition of first order.Comment: 23 pages, 14 figures; matches published version, including Erratum. Conclusions, pictures, numerics remained unchange

N=1 super-Chern-Simons coupled to parity-preserving matter from Atiyah-Ward space-time

In this letter, we present the Parkes-Siegel formulation for the massive Abelian $N$$=$$1$ super-{\QED} coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from ($2$$+$$2$) to ($1$$+$$2$) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the ${\tau}_{3}$QED$_{1+2}$ coupled to a Chern-Simons term naturally comes out.Comment: 7 pages, latex, no figure

Dynamics of Higher Spin Fields and Tensorial Space

The structure and the dynamics of massless higher spin fields in various dimensions are reviewed with an emphasis on conformally invariant higher spin fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal higher spin fields constitute the quantum spectrum of a twistor-like particle propagating in tensorial spaces of corresponding dimensions. We give a detailed analysis of the field equations of the model and establish their relation with known formulations of free higher spin field theory.Comment: JHEP3 style, 40 pages; v2 typos corrected, comments and references added; v3 published versio

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 twistor-like spinor variables. The D=4 model contains a continuous real parameter $a\geq 0$ 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 of ref. [1] (hep-th/9811022) 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 those 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 seven-sphere.Comment: 32 pages, LATEX, no figure

Gravitational anomaly and fundamental forces

I present an argument, based on the topology of the universe, why there are three generations of fermions. The argument implies a preferred gauge group of SU(5), but with SO(10) representations of the fermions. The breaking pattern SU(5) to SU(3)xSU(2)xU(1) is preferred over the pattern SU(5) to SU(4)xU(1). On the basis of the argument one expects an asymmetry in the early universe microwave data, which might have been detected already.Comment: Contribution to the 2nd School and Workshop on Quantum Gravity and Quantum Geometry. Corfu, september 13-20 2009. 10 page

Unification of gauge couplings and the tau neutrino mass in Supergravity without R-parity

Minimal R-parity violating supergravity predicts a value for $alpha_s(M_Z)$ smaller than in the case with conserved R-parity, and therefore closer to the experimental world average. We show that the R-parity violating effect on the $alpha_s$ prediction comes from the larger two-loop b-quark Yukawa contribution to the renormalization group evolution of the gauge couplings which characterizes R-parity violating supergravity. The effect is correlated to the tau neutrino mass and is sensitive to the initial conditions on the soft supersymmetry breaking parameters at the unification scale. We show how a few percent effect on $alpha_s(M_Z)$ may naturally occur even with tau neutrino masses as small as indicated by the simplest neutrino oscillation interpretation of the atmospheric neutrino data from Super-Kamiokande.Comment: Latex, 21 pages including 2 figure