Geometric construction of extended supergravity

Thesis/Dissertation · Thu Dec 31 23:00:00 EST 1981

OSTI ID:5984538

Kostelecky, V A

This work describes the explict construction of the locally SO(4)-invariant, on-shell de Sitter supergravity. First, aspects of classical differential geometry used in the construction of local gauge theories are reviewed. Emphasis is placed on fiber bundles and their uses in Yang-Mills and Einstein theories. Next, the extension of the formalism to differential supergeometry is outlined. Applications to extended supergravities are discussed. Finally, the O(4) deSitter supergravity is obtained by considering a bundle of frames constructed using the orthosymplectic superalgebra osp(4/4). The structure group of this bundle is Sl(2C) x SO(4) and the tangent space to the base supermanifold is homeomorphic to the coset osp(4/4)/sl(2C) x so(4). Constraints taken into the Bianchi identifies yield a realization of the superalgebra in the function space of connections, vielbeins, curvatures and torsions of the bundle. Auxiliary fields, transformation laws and equations of motion are determined. Consistency of the realization is verified, proving closure of the algebra. The associated Poincare supergravity is obtained by a contraction.

• Research Organization: Yale Univ., New Haven, CT (USA)
• OSTI ID: 5984538
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
DIFFERENTIAL EQUATIONS
EINSTEIN-SCHROEDINGER THEORY
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
LIE GROUPS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
SO GROUPS
SUPERGRAVITY
SYMMETRY GROUPS
TRANSFORMATIONS
UNIFIED-FIELD THEORIES
YANG-MILLS THEORY