Hermann Nicolai

On the quantum mechanics of supermembranes

Abstract We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only if the wave function is a singlet under supersymmetry transformations of the nonzero modes. We exhibit the complexity of the supermembrane ground state and examine various truncations of these models. None of these truncations has massless states.

N=8 Supergravity

Abstract The complete structure of N = 8 supergravity is presented with an optional local SO(8) invariance. The SO(8) gauge interactions break E 7 invariance, but leave the local SU(8) unaffected. Exploiting E 7 × SU(8) invariance and using explicit lowest order results, we first derive the complete action and transformation laws. Subsequently, we introduce local SO(8) invariance and prove the consistency of the theory. Possible implications of our results are discussed.

Conformal Symmetry and the Standard Model

We re-examine the question of radiative symmetry breaking in the Standard Model in the presence of right-chiral neutrinos and a minimally enlarged scalar sector. We demonstrate that, with these extra ingredients, the hypothesis of classically unbroken conformal symmetry, besides naturally introducing and stabilizing a hierarchy, is compatible with all available data; in particular, there exists a set of parameters for which the model may remain viable even up to the Planck scale. The decay modes of the extra scalar field provide a unique signature of this model which can be tested at LHC.

Maximal gauged supergravity in three dimensions

We construct maximally supersymmetric gauged N = 16 supergravity in three dimensions, thereby obtaining an entirely new class of anti--de Sitter supergravities. These models apparently cannot be derived from any known higher-dimensional theory and point to the existence of a new type of supergravity beyond D = 11. One of their noteworthy features is a non-Abelian generalization of the duality between scalar and vector fields in three dimensions. Among the possible gauge groups, SO(8) x SO(8) is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as F(4(-20)) x G2.

N=8 supergravity with local SO(8) × SU(8) invariance

We present an extension of N=8 supergravity in which the natural symmetry group SO(8) is gauged. Local SO(8) invariance is shown to be consistent with the dynamically realized SU(8) symmetry. We mention possible implications of this result for superunification.

Gauged supergravities, tensor hierarchies, and M-theory

Deformations of maximal supergravity theories induced by gauging non-abelian subgroups of the duality group reveal the presence of charged M-theory degrees of freedom that are not necessarily contained in supergravity. The relation with M-theory degrees of freedom is confirmed by the representation assignments under the duality group of the gauge charges and the ensuing vector and tensor gauge fields. The underlying hierarchy of these gauge fields is required for consistency of general gaugings. As an example gauged maximal supergravity in three space-time dimensions is presented in a version where all possible tensor fields appear.

On a new characterization of scalar supersymmetric theories

Abstract It is shown that scalar and possibly other supersymmetric theories are characterized by the existence of a transformation of the Bose fields with the property that the image of the full bosonic action is the free action and the Jacobi-determinant of the transformation equals the Matthews-Salam-Seiler determinant of the model. Some possible implications of this result are discussed.

Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions

We present the maximally supersymmetric three-dimensional gauged supergravities. Owing to the special properties of three dimensions | especially the on-shell duality between vector and scalar elds, and the purely topological character of (super)gravity | they exhibit aneven richer structure than the gauged supergravities in higher dimensions. The allowed gauge groups are subgroups of the global E8(8) symmetry of ungauged N = 16 supergravity. They include the regular series SO(p;8 p)SO(p;8 p) for all p =0 ; 1;:::;4, the group E8(8) itself, as well as various noncompact forms of the exceptional groups E7;E6and F4 G2. We show that all these theories admit maximally supersymmetric ground states, anddetermine their backgroundisometries, which aresuperextensions oftheanti-de Sitter group SO(2;2). The very existence of these theories is argued to point to a new supergravity beyond the standard D=11supergravity.

Hyperbolic Kac-Moody algebras and chaos in Kaluza-Klein models

Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinskii, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike (“cosmological”) singularity disappears in spacetime dimensions D ≡ d + 1 > 10. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac–Moody algebra. In this Letter we show that the same connection applies to pure gravity in any spacetime dimension 4, where the relevant algebras are AEd . In this way the disappearance of chaos in pure gravity models in D 11 dimensions becomes linked to the fact that the Kac–Moody algebras AEd are no longer hyperbolic for d 10.  2001 Elsevier Science B.V. All rights reserved.

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.