Lifting Klein-Gordon/Einstein solutions to general nonlinear sigma-models: the wormhole example

Philippe Brax, C. P. Burgess, F. Quevedo

Research output: Contribution to journalArticlepeer-review


We describe a simple technique for generating solutions to the classical field equations for an arbitrary nonlinear sigma-model minimally coupled to gravity. The technique promotes an arbitrary solution to the coupled Einstein/Klein-Gordon field equations for a single scalar field σ to a solution of the nonlinear sigma-model for N scalar fields minimally coupled to gravity. This mapping between solutions does not require there to be any target-space isometries and exists for every choice of geodesic computed using the target-space metric. In some special situations — such as when the solution depends only on a single coordinate (e.g. for homogeneous time-dependent or static spherically symmetric configurations) — the general solution to the sigma-model equations can be obtained in this way. We illustrate the technique by applying it to generate Euclidean wormhole solutions for multi-field sigma models coupled to gravity starting from the simplest Giddings-Strominger wormhole, clarifying why in the wormhole case Minkowski-signature target-space geometries can arise. We reproduce in this way the well-known axio-dilaton string wormhole and we illustrate the power of the technique by generating simple perturbations to it, like those due to string or α′ corrections.

Original languageEnglish (US)
Article number130
JournalJournal of High Energy Physics
Issue number2
StatePublished - Feb 2024


  • Axions and ALPs
  • Duality in Gauge Field Theories
  • Effective Field Theories
  • Sigma Models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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