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arXiv · 2406.17922

On induced L-infinity action of diffeomorphisms on Cochains

Andrey Losev·Dmitrii Sheptunov·Xin Geng
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Abstract

One of the approaches to quantum gravity is to formulate it in terms of De Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue of general relativity is the action of diffeomorphisms of space-time on fields. In this paper, we induce the action of diffeomorphisms on cochains by homotopy transfer (or, equivalently, BV integral) that leads to a $L_{\infty}$ action. We explicitly compute this action for the space-time being an interval, a circle, and a square.

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Andrey Losev, Dmitrii Sheptunov, Xin Geng. 2024-06-25. On induced L-infinity action of diffeomorphisms on Cochains. https://doi.org/10.1016/j.geomphys.2025.105723

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