Space-time supersymmetry of the covariant superstring

We explicitly derive the ghost oscillator contribution to the gauge covariant fermion emission vertex. This vertex is used to construct the space-time supersymmetry transformation laws which are shown to be an invariance of the free gauge covariant action of the superstring. We develop methods to deal with the quadratic exponentials which appear in the fermion emission vertex, in order to study the closure of the supersymmetry algebra. As a by-product, we complete the proof of the equivalence between the “old” and “new” formulations of the superstring.     

The exceptional Jordan algebra and the superstring

Two representations of the exceptional Jordan algebra are presented, one in terms of bose vertex operators, and the other in terms of superstring vertex operators in bosonised form, including their BRST ghost contributions. It is also shown how the non-exceptional Jordan algebras may be constructed similarly.     

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism and the pure gauge theory reduces to a Higgs model in lower dimensions.Laboratoire propre du C.N.R.S. associé à l'Ecole Normale Supérieure et à l'Université de Paris Sud     

Space-time supersymmetry in covariant superstring field theory

It is shown that the existence of a transition operator, which interchanges the BRS charges of the Neveu-Schwarz and the Ramond sectors, implies space-time supersymmetry in the covariant free open superstring field theory proposed previously by the present authors.     

Perturbative BPS algebras in superstring theory

This paper investigates the algebraic structure that exists on perturbative BPS states in the superstring, compactified on the product of a circle and a Calabi-Yau fourfold. This structure was defined in a recent article by Harvey and Moore. It is shown that for a toroidal compactification this algebra is related to a generalized Kac-Moody algebra. The BPS algebra itself is not a Lie algebra. However, it turns out to be possible to construct a Lie algebra with the same graded dimensions, in terms of a half-twisted model. The dimensions of these algebras are related to the elliptic genus of the transverse part of the string algebra. Finally, the construction is applied to an orbifold compactification of the superstring.     

Differential calculus on Jordan algebras and Jordan modules

Having in mind applications to particle physics we develop the differential calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on differential calculus over the exceptional Jordan algebra and provide a complete characterization of the theory of connections for free Jordan modules.

     

Superconformal deformation,zero-norm states and space-time symmetries of the superstring theories

We present a formalism to study type II and Heterotic superstrings with massless and massive background fields in the bosonic sector. This formalism is appropriate to study high energy symmetries of the superstring. As an example, we explicitly relate all massless symmetries to the massless zero-norm states in the spectrum. This includes theE ₈ ?E ₈ andSO (32) gauge symmetries in the ten-dimensional Heterotic string. The first (evenG-parity) massive level is briefly described. We then argue the existence of new symmetries for the massive Yang-Mills-like gauge bosons and tensor fields at each fixed mass level. These enlarged stringy symmetries correspond to the decoupling of massive zero-norm states in the spectrum.     

The role of classical symmetries in the low-energy limit of superstring theories

Due to the appearance of certain classical symmetries in the low-energy limit of superstring theories, some relevant parameters remain undetermined. The breakdown of these symmetries is investigated in the loop expansion. This then enables one to clarify which properties of the low-energy theory are artifacts of the classical approximation. The results are relevant for the relations between gauge coupling constants and the magnitude of the supersymmetry breakdown scale.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.     

Quantum measures and states on Jordan algebras

A problem of Mackey for von Neumann algebras has been settled by the conjunction of the early work of Gleason and the recent advances of Christensen and Yeadon. We show that Mackey's conjecture holds in much greater generality. LetA be a JBW-algebra and letL be the lattice of all projections inA. A quantum measure onL is a countably additive map,m, fromL into the real numbers. Our results imply thatm always has a unique extension to a bounded linear functional onA, provided thatA has no TypeI ₂ direct summand.     

Freely acting Z3 symmetries of a Yau manifold and three-generation superstring models

We identify the various freely acting non-conjugate Z₃ symmetries of a Yau manifold defined by polynomials of bidegree (3, 0), (0, 3) and (1, 1) in CP³ × CP³. Compactification of the ten-dimensional heterotic superstring theory on this manifold, after dividing the latter out by one of these Z₃'s, gives rise to three physically distinct three-generation superstring models. One of them has not been previously identified and we discuss its residual four-dimensional discrete symmetries.     

Generalized symmetries and deformations of the direct sums of Lie algebras

The problem of the combined space-time and internal symmetry of elementary Particles is investigated from the view-point of the Lie algebras deformation theory. It is demonstrated that the deformations of the direct sum of the Poincaré and internal symmetry algebras conserve the structure of the direct sum, if the internal symmetry is semi-simple or is described by the special type of algebras with abelian ideal. So the internal and space-time characteristics of the system remain independent.     

Description of a class of superstring compactifications related to semi-simple Lie algebras

A class of vacuum configurations in the superstring theory obtained by compactification of physical dimensions from ten to four is constructed. The compactification scheme involves taking quotients of tori of semisimple Lie algebras by finite symmetry group actions. The complete list of such configurations arising from actions by a Coxeter transformation is given. Some topological invariants having physical interpretations are calculated.