Higher-dimensional self-consistent solution with deformed internal space

Journal Article · Wed Jul 15 04:00:00 EDT 1987 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.36.397· OSTI ID:6347310

Shen, T C; Sobczyk, J

We study a system of gravity and free massless scalar fields minimally coupled to gravity in a 7-dimensional background which is a direct product of a 4-dimensional Minkowski space and a 3-dimensional homogeneously deformed three-sphere. Compactification is caused by the vacuum energy of scalar fields. The effective potential as a function of two parameters (scale and deformation) is calculated numerically after dimensional regularization. We find the effective potential decreases rapidly toward negative infinity in both prolate and oblate directions. The classical curvature, however, can balance the quantum effect and yields three extrema. In addition to the round S/sup 3/ solution in the quantum-corrected field equations, we find two deformed ones. One of the deformed solutions corresponds to the local minimum of the total potential. The round three-sphere solution, however, corresponds to the local maximum of that. More scalar fields can enlarge the scale of the internal space but not affect the shape. This serves as an example of gauge symmetry breaking by deformation of the internal space in multidimensional theories. The stability of these background solutions is discussed but not established conclusively. A discussion of four different analytic-continuation procedures is presented in one of the appendixes.

• Research Organization: International School for Advanced Studies, 34014 Trieste, Italy
• OSTI ID: 6347310
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 36:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

640106 -- Astrophysics & Cosmology-- Cosmology
645400* -- High Energy Physics-- Field Theory
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMOLOGICAL MODELS
COUPLING
ELEMENTARY PARTICLES
FIELD THEORIES
GRAND UNIFIED THEORY
GRAVITATIONAL FIELDS
KALUZA-KLEIN THEORY
LIE GROUPS
MANY-DIMENSIONAL CALCULATIONS
MASSLESS PARTICLES
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
MINKOWSKI SPACE
NUMERICAL ANALYSIS
PARTICLE MODELS
SCALAR FIELDS
SEMICLASSICAL APPROXIMATION
SPACE
SPACE-TIME
SU GROUPS
SU-2 GROUPS
SUPERGRAVITY
SYMMETRY BREAKING
SYMMETRY GROUPS
U GROUPS
U-1 GROUPS
UNIFIED GAUGE MODELS
UNIFIED-FIELD THEORIES
VACUUM STATES