Conformal invariance beyond the leading order in the supersymmetric nonlinear. sigma. model with dilaton

Journal Article · Sat Dec 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.4094· OSTI ID:5756541

Diamandis, G A; Georgalas, B C; Lahanas, A B ^[1]

---

1. Physics Department, Nuclear and Particle Physics Section, University of Athens, Panepistimiopolis, Athens 157-71 (Greece)

We calculate the {ital O}({alpha}{prime}{sup 3}) contributions to the renormalization-group {beta} functions in the {ital N}=1 supersymmetric {sigma} model with a dilaton. At this order both metric and dilaton {beta} functions are found to depend nontrivially on the dilaton field and vanish if the dilaton satisfies {del}{sub {mu}}{del}{sub {nu}}{phi}=0. By employing the Curci-Paffuti relation it is shown that such dilaton backgrounds in Ricci-flat spaces {ital R}{sub {mu}{nu}}=0 satisfy the conformal invariance conditions up to this order. The particular class of Ricci-flat, compact, and orientable manifolds naturally emerge as appropriate internal-space configurations consistent with local scale invariance. We further explore the cosmological consequences of these dilaton configurations. In a Robertson-Walker four-dimensional background we find all dilatons satisfying {del}{sub {mu}}{del}{sub {nu}}{phi}=0. Except for the constant and the time-dependent dilaton {phi}({ital t})={minus}2 ln{ital t}+{lambda} whose cosmological implications have been already discussed in the literature, additional solutions are found. These may be of relevance beyond leading order and for nonvanishing background values for the antisymmetric tensor {ital B}{sub {mu}{nu}}. For these solutions, also the cosmic scale factor is at most linear in time therefore giving rise to either a static or a linearly expanding (contracting) universe.

• OSTI ID: 5756541
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:12; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

640106* -- Astrophysics & Cosmology-- Cosmology
645300 -- High Energy Physics-- Particle Invariance Principles & Symmetries
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFORMAL INVARIANCE
COSMOLOGICAL MODELS
ENERGY-MOMENTUM TENSOR
FOUR-DIMENSIONAL CALCULATIONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATRICES
PARTICLE MODELS
RENORMALIZATION
S MATRIX
SIGMA MODEL
SUPERSYMMETRY
SYMMETRY
TENSOR FORCES
TENSORS
UNIVERSE