Emergent Lorentzian dispersion relations from a Euclidean scalar-tensor theory
Can one be fooled into thinking that space and time are fundamentally described by a Lorentzian manifold? In this article, we describe a scenario in which a theory constructed on a (Euclidean signature) Riemannian manifold can lead to degrees of freedom with Lorentzian dispersion relations, due to a nontrivial configuration of a scalar field. In particular, we perform a perturbative analysis of a renormalizable shift-symmetric scalar-tensor theory and find that it can, in principle, admit a massless tensor degree of freedom with a Lorentzian dispersion relation. While the remaining degrees of freedom in the gravity sector will, in general, satisfy Euclidean dispersion relations, we argue that they can be brought under control by elliptic equations with an appropriate choice of boundary conditions.
Authors
- Sante Carloni (ORCID: https://orcid.org/0000-0003-2373-2653)
- Shinji Mukohyama (ORCID: https://orcid.org/0000-0002-9934-2785)
- Karl J. Friston
Institutions
- Kavli Institute for the Physics and Mathematics of the Universe (JP)
- Central European University (AT)
- Charles University (CZ)
- Kyoto University (JP)
- Instituto de Física Teórica (ES)
- Istituto Nazionale di Fisica Nucleare, Sezione di Genova (IT)
- Institute of Physics of the Slovak Academy of Sciences (SK)
- Yukawa Institute for Theoretical Physics (JP)
- The University of Tokyo (JP)
- University of Genoa (IT)
Publication Details
- Journal
- Physical review. D/Physical review. D.
- Published
- 2025-07-05
- DOI
- https://doi.org/10.1103/zylg-s8lf
- Primary Topic
- Cosmology and Gravitation Theories
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministry of Education, Culture, Sports, Science and Technology
- Ministerstvo Školství, Mládeže a Tělovýchovy
- National Taiwan University
- Japan Society for the Promotion of Science