Superspace geometry from D = 4, N = 1 heterotic superstrings

The presence of classical κ-supersymmetry invariance is shown to be consistent with an off-shell D = 4, N = 1 conformal supergravity background in the presence of a tensor multiplet. We derive a suitable set of constraints, via super Weyl rescaling, for a heterotic superstring in such a background. Starting from the geometry of 16-16 supergravity and gauging the R-symmetry with a composite connection, we derive a geometrical structure similar to that of new minimal supergravity.     

p-adic superstrings

Different possibilities to construct p-adic superstring amplitudes are discussed. To describe one of these possibilities we formulate a p-adic generalization of the conformal technique. p-adic conformal rules allow us to explicitly write down the amplitude for massless particles. They do not have the form of the usual kinematical factors multiplied by the p-adic modification of the usual amplitudes. The relation between open and closed p-adic superstring amplitudes is discussed.     

Jack Polynomials in Superspace

This work initiates the study of orthogonal symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were constructed. Orthogonal eigenfunctions are now obtained by diagonalizing the first nontrivial element of a bosonic tower of commuting conserved charges not containing this Hamiltonian. Quite remarkably, the expansion coefficients of these orthogonal eigenfunctions in the supermonomial basis are stable with respect to the number of variables. The second and more direct approach amounts to symmetrize products of non-symmetric Jack polynomials with monomials in the fermionic variables. This time, the orthogonality is inherited from the orthogonality of the non-symmetric Jack polynomials, and the value of the norm is given explicitly.     

Rigid superstrings

A recently proposed bosonic string action containing a term proportional to the world sheet is supersymmetrized in the light-cone gauge. We compute the one-loop contribution to the β function of the new coupling constant and find that the asymptotic freedom present in the bosonic case is not destroyed by the addition of the fermionic degrees of freedom.     

Finitary Algebraic Superspace

An algebraic scheme is suggested in whichdiscretized spacetime turns out to be a quantumobservable. As an example, a toy model producingspacetimes of four points with different topologies ispresented. The possibility of incorporating this schemeinto the framework of noncommutative differentialgeometry is discussed.     

Cosmic superstrings II

Modern string theory provides a rich array of objects which could potentially appear as cosmic strings in our observable four-dimensional universe. However, there are many possible decay modes which would prevent the appearance of such strings. We investigate the conditions under which metastable strings can exist, and we find that such strings are present in many models. Hence cosmic strings give a potentially large window into string physics. To cite this article: E.J. Copeland et al., C. R. Physique 5 (2004).

Résumé

La théorie moderne des supercordes fournit un choix riche d'objets qui pourraient potentiellement apparaître en tant que cordes cosmiques dans notre univers quadridimensionnel observable. Cependant, il y a beaucoup de modes possibles de désintégration qui empêcheraient l'apparition de telles cordes. Nous étudions les conditions dans lesquelles des cordes métastables peuvent exister, et nous constatons que de telles cordes sont présentes dans beaucoup de modèles. Par conséquent les cordes cosmiques ouvrent une fenêtre potentiellement grande vers la physique des supercordes. Pour citer cet article : E.J. Copeland et al., C. R. Physique 5 (2004).     

Supercompositeness from superstrings

String Unified Models based on the k = 1 level of the Kac-Moody Algebra, predict the existence of “exotic” new states which carry fractional electric charges. We analyse the possibility of considering these “exotics” as preonic matter which can be used to form the families and the gauge group breaking higgs scalars. It is proposed that such a formation may occur provided that these states transform non-trivially under a non-Abelian gauge group with a relatively large rank in order to confine them at a sufficiently large scale. Such a situation is natural in string derived unified models, since the role of the confining group can be played by (part of) the Hidden symmetry. As an example, we present a string derived toy model based on the SU(4) × SU(2) _L × SU(2) _R Pati-Salam gauge group.     

Inflation with superstrings

Cosmological solutions with three exponentially expanding space dimensions in the N=1 supersymmetric Yang-Mills supergravity system are found under the assumption of gluino and “subgravitino” condensation. The potential has a long flat region providing sufficient inflation.     

Thermodynamics of superstrings

We study the thermal properties and the thermodynamical equilibrium fluctuations of a gas of massive heterotic string excitations at Planck energy scales. The behavior of this system parallels in several ways that of massive Schwarzschild black holes. We briefly comment on its possible influence on primeval entropy generation.     

Effects of superstrings in collisions

Superstring theory in d = 10 dimensions after Calabi—Yau compactification yields a minimum low-energy gauge group SU(3)_C × SU(2)_L × U(1)_Y × U(1)_E. The low-energy theory includes particles with the quantum numbers of 27 representations of E₆, each of which contains an extra neutrino ν^c conventionally called a “right-handed neutrino”. The contributions of ν and ν^c to through Z⁰ and Z_E mixing is calculated. Small contributions are found of the new right-handed neutrino and of the superstring boson Z_E to σ(e⁺e⁻ → γ + nothing).     

On supersymmetry breaking in superstrings

We prove that the existence of a slightly massive or gravitino or gaugino in a class of gaussian string compactifications, implies the existence of an entire tower of such states below M_Planck, signaling the approach to a limit of decompactification.     

Superspace formulation of supergravity

A geometrical interpretation of supergravity is given in terms of the differential geometry of superspace. Starting from a general affine superspace, the geometry is specified in such a way as to contain as a special case the superspace of a global supersymmetry. Covariant equations are given which are equivalent to those of supergravity in four-space. The question of finding a suitable Lagrangian is discussed.     

Superspace formulation of supergravity

The recent superspace formulations of supergravity using vierbeins are shown to be equivalent to the previous metric tensor superspace formulation of the authors for physical (mass-shell) spaces. An alternate method of gauge completing the vierbein without using Breitenlohner fields is given to the order necessary to generate field equations, and again shown dynamically equivalent to the above formulations.     

The Superspace of geometrodynamics

Wheeler’s Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity. I dedicate this contribution to the scientific legacy of John Wheeler.