Gravity and generalised geometry from a Lie 2-algebroid perspective
Abstract
We revisit the problem of defining natural torsion and curvature tensors for generalised connections and of using them to reconstruct the effective action for the massless modes of the closed string from generalised geometry. The starting point is the description of a Courant algebroid as a differential graded (dg) symplectic manifold. A systematic procedure for split dg manifolds singles out a generalised Lie bracket as part of a larger Lie 2-algebroid structure, with the right properties to unambiguously define torsion and Riemann curvature tensors together with their corresponding Bianchi identities. This framework eliminates the structural circularity and ambiguity problems of previous approaches in the literature. We show that a unique generalised metric compatible generalised connection with fixed (con)torsion exists for any choice of ordinary connection that splits the dg manifold, while at the same time all Lie 2-algebroids obtained in this way are equivalent up to L∞ quasi-isomorphisms. For a given Lie 2-algebroid we demonstrate that the unique compatible generalised connection reproduces the effective closed string action from a geometric action based on the new generalised Ricci tensor upon making a canonical choice of torsion.
Related
- Transposed Poisson structures in graded and algebroid geometry
- Einstein-Cartan and Palatini-Cartan Gravity from Graded Poisson Geometry
- A De Rham Perspective on the Symplectic Geometry of Teichmüller Space
- Algebroid Desingularizable Poisson Structures
- Parabolic Lie algebroid connections on parabolic principal bundles over curves
BibTeX
@misc{chatzistavrakidis2026gravity,
title = {{Gravity and generalised geometry from a Lie 2-algebroid perspective}},
author = {Athanasios Chatzistavrakidis and Chris Hull and Larisa Jonke and Sylvain Lavau and Peter Schupp},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01292},
eprint = {2610.01292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01292},
}
RIS
TY - UNPB
TI - Gravity and generalised geometry from a Lie 2-algebroid perspective
AU - Athanasios Chatzistavrakidis
AU - Chris Hull
AU - Larisa Jonke
AU - Sylvain Lavau
AU - Peter Schupp
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01292
UR - https://arxiv.org/abs/2610.01292
AB - We revisit the problem of defining natural torsion and curvature tensors for generalised connections and of using them to reconstruct the effective action for the massless modes of the closed string from generalised geometry. The starting point is the description of a Courant algebroid as a differential graded (dg) symplectic manifold. A systematic procedure for split dg manifolds singles out a generalised Lie bracket as part of a larger Lie 2-algebroid structure, with the right properties to unambiguously define torsion and Riemann curvature tensors together with their corresponding Bianchi identities. This framework eliminates the structural circularity and ambiguity problems of previous approaches in the literature. We show that a unique generalised metric compatible generalised connection with fixed (con)torsion exists for any choice of ordinary connection that splits the dg manifold, while at the same time all Lie 2-algebroids obtained in this way are equivalent up to L_∞ quasi-isomorphisms. For a given Lie 2-algebroid we demonstrate that the unique compatible generalised connection reproduces the effective closed string action from a geometric action based on the new generalised Ricci tensor upon making a canonical choice of torsion.
ER -