S7S^7 Current Algebras

We present $S^7$-algebras as generalized Kac-Moody algebras. A number of free-field representations is found. We construct the octonionic projective spaces {\O}P^N.Comment: 11 pages, phyzzx and epsf, HUB-IEP-94/1, G\"oteborg-ITP-94-

The Seven-sphere and its Kac-Moody Algebra

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appende

Quaternionic Superconformal Field Theory

We develop a superfield formalism for N=4 superconformal two-dimensional field theory. A list is presented of minimal free superfields, i.e. of multiplets containing four bosons and four fermions. We show that the super-Poincar\'e algebra of the six-dimensional superstring in the light-cone gauge is essentially equivalent to a local N=4 superconformal symmetry, and outline the construction of octonionic superconformal field theory.Comment: 31 pages, phyzzx, G\"oteborg-ITP-92-4

On a possible new R^2 theory of supergravity

We consider a new MacDowell-Mansouri R^2-type of supergravity theory, an extension of conformal supergravity, based on the superalgebra Osp(1|8). Invariance under local symmetries with negative Weyl weight is achieved by imposing chirality-duality and double-duality constraints on curvatures, along with the usual constraint of vanishing supertorsion. An analysis of the remaining gauge symmetries shows that those with vanishing Weyl weight are invariances of the action at the linearized level. For the symmetries with positive Weyl weight we find that invariance of the action would require further modifications of the transformation rules. This conclusion is supported by a kinematical analysis of the closure of the gauge algebra.Comment: 52 pages, Late

S 7 and. . .

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moodylike algebra. Covariance properties and tensorial composition of spinors under S 7 are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given. published in Commun.Math.Phys. 167 (1995) 373. ? e-mail [email protected] y e-mail [email protected] M. Cederwall and C.R. Preitschopf, "S 7 and c S 7 " 1. Preliminaries. This paper is devoted to an investigation of the seven-sphere as a manifold equipped with group-like multiplication, and to its extension to a Kac-Moody-like algebra. As is well known, the seven-..

N = 8 Superconformal Algebra and the Superstring

The superstring in D=3; 4 and 6 is invariant under an N=D\Gamma2 superconformal algebra based on d S D\Gamma3 . There is a direct relationship between this (world-sheet) symmetry and the super-Poincar'e (target space) symmetry. We establish this relationship using the light-cone gauge, show how the statement generalizes to D= 10 and examine the properties of the N = 8 superconformal algebra and the possible implications of its existence. Published in Phys.Lett. 311B (1993) 76. In order to understand the physics of a certain model, we need to find its symmetries. The crucial step in the Veneziano model [1] was the discovery of the Virasoro algebra [2], the infinite-dimensional conformal symmetry. It led to the no-ghost theorem, and in the modern era it has been used e.g. to construct string field theory. It was also the extension of this symmetry to the superconformal one by Ramond [3] that led to the Ramond-Neveu-Schwarz model [3,4] we use today. However, in this formalism global ..