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- W2031583929 abstract "In a nonlinear ensuremath{sigma} model coupled to gravity we compute all one-loop divergences including contributions from both virtual gravitons and scalars ${mathrm{ensuremath{varphi}}}^{mathit{i}}$ which are valued on an internal manifold 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 ensuremath{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 M plays no important role in improving the ultraviolet behavior of the model. As regards the ensuremath{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 ${mathit{g}}_{mathrm{ensuremath{mu}}ensuremath{nu}}$, the rest inducing renormalizations of the manifold metric ${mathit{scrG}}_{mathit{i}mathit{j}}$ and the potential V not depending on the four-dimensional geometry. Up to terms logarithmic in the momentum cutoff scale ensuremath{Lambda} having the structure (${mathrm{ensuremath{partial}}}_{mathrm{ensuremath{Gamma}}}$ensuremath{varphi}${)}^{4}$, (${mathit{scrD}}_{mathrm{ensuremath{mu}}}$${mathit{scrD}}_{ensuremath{nu}}$ensuremath{varphi}${)}^{2}$ the resulting one-loop effective theory is of the same form as the tree-level Lagrangian with the renormalized metric ${mathit{scrG}}_{mathit{i}mathit{j}}$ and potential V." @default.
- W2031583929 created "2016-06-24" @default.
- W2031583929 creator A5010522290 @default.
- W2031583929 creator A5035189946 @default.
- W2031583929 creator A5043174393 @default.
- W2031583929 creator A5059613678 @default.
- W2031583929 date "1990-07-15" @default.
- W2031583929 modified "2023-10-11" @default.
- W2031583929 title "Ultraviolet behavior of four-dimensional σ models coupled to gravity" @default.
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- W2031583929 doi "https://doi.org/10.1103/physrevd.42.469" @default.
- W2031583929 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/10012864" @default.
- W2031583929 hasPublicationYear "1990" @default.
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