Ultraviolet behavior of four-dimensional. sigma. models coupled to gravity

Journal Article · Sun Jul 15 00:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.469· OSTI ID:6687306

Chiou-Lahanas, C; Kapella-Economou, A; Lahanas, A B; Maintas, X N ^[1]

---

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

In a nonlinear {sigma} model coupled to gravity we compute all one-loop divergences including contributions from both virtual gravitons and scalars {phi}{sup {ital i}} which are valued on an internal manifold {ital M}. The calculation is performed in arbitrary curved backgrounds and it is useful not only for studying the renormalization properties of this particular gravity theory but also for constructing the effective {sigma}-model Lagrangian incorporating the dominant one-loop effects near the Planck scale. The latter may be of relevance to low-energy effective theories inspired by some string models. We find that the geometry of the manifold {ital M} plays no important role in improving the ultraviolet behavior of the model. As regards the {sigma}-model effective-Lagrangian calculation we have found that a large portion of the dominant radiative effects can be absorbed by a redefinition of the four-dimensional metric {ital g}{sub {mu}{nu}}, the rest inducing renormalizations of the manifold metric {ital scrG}{sub {ital i}{ital j}} and the potential {ital V} not depending on the four-dimensional geometry. Up to terms logarithmic in the momentum cutoff scale {Lambda} having the structure ({partial derivative}{sub {Gamma}}{phi}){sup 4}, ({ital scrD}{sub {mu}}{ital scrD{nu}}{phi}){sup 2} the resulting one-loop effective theory is of the same form as the tree-level Lagrangian with the renormalized metric {ital scrG}{sub {ital i}{ital j}} and potential {ital V}.

• OSTI ID: 6687306
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:2; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645300 -- High Energy Physics-- Particle Invariance Principles & Symmetries
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
COUPLING
ELEMENTARY PARTICLES
EXTENDED PARTICLE MODEL
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
GRAVITATIONAL FIELDS
GRAVITATIONAL RADIATION
GRAVITONS
HIGGS BOSONS
LAGRANGIAN FUNCTION
MASSLESS PARTICLES
MATHEMATICAL MODELS
METRICS
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
RADIATIONS
RENORMALIZATION
SIGMA MODEL
SPACE-TIME
STRING MODELS
SUPERSYMMETRY
SYMMETRY
SYMMETRY BREAKING
ULTRAVIOLET DIVERGENCES