Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
PreprintarXiv licencearXiv

A gravitational realization of Courant--Hilbert deformations

  • Osamu Fukushima
  • Miyabi Kurihara
  • Takaki Matsumoto
  • Kentaroh Yoshida
Open at sourcePDFDOICite

Abstract

Courant--Hilbert (CH) deformations unify broad classes of solvable stress-tensor flows including TT̅ and root-TT̅. However, a gravitational action that systematically yields such general deformations has remained unknown. In this Letter, we construct a two-dimensional massive gravity theory whose on-shell action reproduces the complete CH deformation. The gravity sector is defined via an arbitrary function of the eigenvalue ratio y of the relative zweibein. To bypass the technical difficulty of directly eliminating the auxiliary zweibein, we reformulate the matter sector using a 2 × 2 spectral decomposition involving y and a rank-one projector K. Sequentially solving the equations of motion---first for K and subsequently for y---naturally maps the system onto the Russo-Townsend form of the CH flow. Our work extends Tolley's massive gravity formulation of TT̅ flows to the CH landscape, providing a clear geometric mechanism for solvable stress-tensor flows.

Related

  1. Exact Stress Tensor Flows in Causal Electrodynamics: Courant-Hilbert Approach
    Zahra Pezhman, Komeil Babaei Velni, H. Babaei-Aghbolagh
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
  2. Meromorphic open-string vertex algebras and twisted modules from Courant algebroids
    Qixuan Fang, Fei Qi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  3. Adiabatic Deformations of Black Hole Moduli: II. The Magnetic GHS Family
    Karim Benakli, Anna Chrysostomou
    HALPreprintLicence not statedGravitation & general relativityHigh-energy & particle physicsHAL
  4. Adiabatic Deformations of Black Hole Moduli: I. Canonical Slices and Fredholm Solvability
    Karim Benakli, Anna Chrysostomou
    HALPreprintLicence not statedGravitation & general relativityHigh-energy & particle physicsHAL
  5. Brane-probes response to poly-vector deformations
    Sergei Barakin, Angelina Kurenkova, Edvard T. Musaev
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{fukushima2026gravitational,
  title = {{A gravitational realization of Courant--Hilbert deformations}},
  author = {Osamu Fukushima and Miyabi Kurihara and Takaki Matsumoto and Kentaroh Yoshida},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.35452},
  eprint = {2609.35452},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35452},
}
RIS
TY  - UNPB
TI  - A gravitational realization of Courant--Hilbert deformations
AU  - Osamu Fukushima
AU  - Miyabi Kurihara
AU  - Takaki Matsumoto
AU  - Kentaroh Yoshida
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.35452
UR  - https://arxiv.org/abs/2609.35452
AB  - Courant--Hilbert (CH) deformations unify broad classes of solvable stress-tensor flows including TT̅ and root-TT̅. However, a gravitational action that systematically yields such general deformations has remained unknown. In this Letter, we construct a two-dimensional massive gravity theory whose on-shell action reproduces the complete CH deformation. The gravity sector is defined via an arbitrary function of the eigenvalue ratio y of the relative zweibein. To bypass the technical difficulty of directly eliminating the auxiliary zweibein, we reformulate the matter sector using a 2 × 2 spectral decomposition involving y and a rank-one projector K. Sequentially solving the equations of motion---first for K and subsequently for y---naturally maps the system onto the Russo-Townsend form of the CH flow. Our work extends Tolley's massive gravity formulation of TT̅ flows to the CH landscape, providing a clear geometric mechanism for solvable stress-tensor flows.
ER  -