Anne Taormina

Superconformal Algebras and String Compactification on Manifolds with SU(N) Holonomy

Abstract We discuss string compactifications on manifolds with SU( n ) holonomy by making use of representation theories of extended superconformal algebras. In particular, string compactification on K 3 surfaces is discussed in detail. We calculate loop-space indices and show that all c = 6 superconformal field theories describe string propagation on manifolds with SU(2) holonomy. We study Gepners models based on the tensoring of N = 2 minimal series and point out that some of these models are identified as orbifolds. We also discuss c = 9 superconformal field theories and their relation to Calabi-Yau manifolds.

Consistent Superstrings as Solutions of the D=26 Bosonic String Theory

Abstract Consistent closed ten-dimensional superstrings, i.e., the two N = 1 heterotic strings and the two N = 2 superstrings, are contained in the 26-dimensional bosonic closed string theory. The latter thus appears as the fundamental string theory.

The symmetry of M-theories

We consider the Cartan subalgebra of any very extended algebra Script G+++ where Script G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra, we find that for all very extensions Script G+++ of simple Lie algebras there are theories of gravity and matter, which admit classical solutions carrying representations of the Weyl group of Script G+++. We also identify the T and S-dualities of superstrings and of the bosonic string with Weyl reflections and outer automorphisms of well-chosen very extended algebras and we exhibit specific features of the very extensions. We take these results as indication that very extended algebras underlie symmetries of any consistent theory of gravity and matter, and might encode basic information for the construction of such theory.

On the unitary representations of N=2 and N=4 superconformal algebras

Abstract We discuss the relationship between the unitary representations of N=2 and N=4 superconformal algebras. We describe how the N=4 irreducible representations decompose into those of N=2 algebra. We also describe the modular properties of N=4 superconformal characters.

The fate of the mixmaster behaviour in vacuum inhomogeneous Kaluza-Klein cosmological models☆

Abstract The generic behaviour of vacuum inhomogeneous Kaluza-Klein cosmologies is studied in the vicinity of the cosmological singularity. The collision law for the Kasner exponents is calculated in any number of spatial dimensions d . Its properties are investigated both theoretically and numerically. It is argued that the chaotic oscillatory behaviour disappears for d ⩾ 10. This regime is replaced by the monotonic Kasner behaviour found previously.

On the unitary representations of a class of N = 4 superconformal algebras

We derive properties of unitary highest weight representations of the N = 4 superconformal algebras in 2 dimensions, characterized by two SU(2)Kac-Moody subalgebras. For the range 3 ⩽ c < 6 we can prove that we have constructed all unitary highest weight representations. These reduce in N = 2 to the discrete series. For other values of the parameters we derive bounds on the values of h, and we conjecture that these are complete. This is motivated by explicit constructions of representations for various values of the parameters. For the so-called massless representations we do indeed prove that our treatment is complete.

Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model

The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the two-parameter family of integrable boundary conditions are reviewed and extended. The energy spectrum of the quantized boundary states is computed, firstly by using a bootstrap technique and, subsequently using a WKB approximation. Requiring that the two descriptions of the spectrum agree with one another allows a determination of the relationship between the boundary parameters, the bulk coupling constant, and the two parameters appearing in the reflection factor describing the scattering of the sinh-Gordon particle from the boundary. These calculations had been performed previously for the case in which the boundary conditions preserve the bulk Z2 symmetry of the model. The significantly more difficult case of general boundary conditions which violate the bulk symmetry is treated in this paper. The results clarify the weak-strong-coupling duality of the sinh-Gordon model with integrable boundary conditions.

The overarching finite symmetry group of Kummer surfaces in the Mathieu group M24

A bstractIn view of a potential interpretation of the role of the Mathieu group M24 in the context of strings compactified on K3 surfaces, we develop techniques to combine groups of symmetries from different K3 surfaces to larger ‘overarching’ symmetry groups. We construct a bijection between the full integral homology lattice of K3 and the Niemeier lattice of type

Characters of the N = 4 superconformal algebra with two central extensions

A_1^{24 }

Assembly models for Papovaviridae based on tiling theory.

, which is simultaneously compatible with the finite symplectic automorphism groups of all Kummer surfaces lying on an appropriate path in moduli space connecting the square and the tetrahedral Kummer surfaces. The Niemeier lattice serves to express all these symplectic automorphisms as elements of the Mathieu group M24, generating the ‘overarching finite symmetry group’