Speaker
Description
The Horndeski theory represents the most comprehensive framework within scalar-tensor theories, comprising a single scalar field whose equations of motion are closed up to second-order derivatives. Nonetheless, systematic extensions involving multiple scalar fields remain incomplete: while the general form of the equations of motion for two fields (bi-Horndeski) is established, the overarching action remains undefined; furthermore, for three or more fields, neither the general action nor the equations have been fully elucidated.
This presentation introduces a novel “definition" that characterizes the Horndeski theory independently of the specific form of the action. Specifically, it stipulates the theory through two conditions: (i) closure under invertible pure disformal transformations, and (ii) the inclusion of the minimal (anchor) theory. From this standpoint, the standard single-field Horndeski (i.e., generalized Galileon) action is recovered, excluding boundary terms.
Subsequently, this methodology is extended to encompass multiple fields. By incorporating reversible bi-disformal transformations and minimal multiple theories, a practical pathway for the construction of multi-field models is provided. As a concrete example, the action involving two fields up to the $\mathcal{L}_4$ sector (with the $\mathcal{L}_5$ coupling set to zero) is derived, demonstrating that the additional term aligns with the antisymmetric structure characteristic of the Allys–Akama–Kobayashi (AAK) model. This signifies that structures inherent to multi-field systems, which are challenging to obtain via straightforward multi-Galileon extensions, naturally arise from the perspective of disformal closure. Additionally, the correspondence with established bi-Horndeski equations and prospects for extending to $N\geq3$ are examined.
This is based on 2511.15423.
| Research Area | Gravity: Field theory |
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