Group-geometric methods in supergravity and superstring theories

Journal Article · Sun Mar 29 23:00:00 EST 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92000697· OSTI ID:5397663

Castellani, L ^[1]

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1. Inst. Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria 1, I-10125 Torino (IT)

The purpose of this paper is to give a brief and pedagogical account of the group-geometric approach to (super)gravity and superstring theories. The authors summarize the main ideas and apply them to selected examples. Group geometry provides a natural and unified formulation of gravity and gauge theories. The invariance of both are interpreted as diffeomorphisms on a suitable group manifold. This geometrical framework has a fruitful output, in that it provides a systematic algorithm for the gauging of Lie algebras and the construction of (super)gravity or (super)string Lagrangians. The basic idea is to associate fundamental fields to the group generators. This is done by considering first a basis of tangent vectors on the group manifold. These vectors close on the same algebra as the abstract group generators. The dual basis, i.e. the vielbeins (cotangent basis of one-forms) is then identified with the set of fundamental fields. Thus, for example, the vielbein V{sup a} and the spin connection {omega}{sup ab} of ordinary Einstein-Cartan gravity are seen as the duals of the tangent vectors corresponding to translations and Lorentz rotations, respectively.

• OSTI ID: 5397663
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:8; ISSN 0217-751X; ISSN IMPAE
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FIELD THEORIES
GAUGE INVARIANCE
GEOMETRY
GROUP THEORY
INVARIANCE PRINCIPLES
LIE GROUPS
LORENTZ FORCE
MATHEMATICAL MANIFOLDS
MATHEMATICAL MODELS
MATHEMATICS
PARTICLE MODELS
QUARK MODEL
STRING MODELS
SUPERGRAVITY
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
TENSORS
UNIFIED-FIELD THEORIES
VECTORS