Emergent Curvature from Flat-Space QFTs: A Computational Search for Gravity

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General Relativity (GR) continues to provide an exceptionally accurate description of gravitational phenomena at macroscopic scales. Yet its reconciliation with quantum mechanics remains elusive [1]. A compelling strategy treats GR as a low-energy Effective Field Theory (EFT), seeking its high-energy extension.

Progress in this direction would require matching candidate UV theories to the EFT of gravity by integrating out heavy degrees of freedom. However, such a matching procedure is notoriously difficult, typically done on a case-by-case basis [2], and often considered infeasible for large models.

In this work, we present the first computer-assisted framework for EFT matching of theories involving spin-2 particles. By extending modern EFT toolkits to incorporate gravitational degrees of freedom, we enable systematic exploration of high-energy extensions of gravity within a quantum field theory setting. As a proof-of-concept, we scan a broad class of models featuring a hidden heavy scalar coupled to a spin-2 field. We compute the one-loop contributions to the low-energy gravitational EFT, finding that they can create the leading-order self-interactions of GR, responsible for inducing curvature.

The extended toolkits employ competing methods for matching. The first – Matchmakereft [3] – uses a diagrammatic method, while the second – Matchete [4] – uses a functional method. The results of the two methods are compared and are found to be identical, with each method offering different insights regarding the origin of the contributions to each term in the EFT.

Our computational approach reveals new patterns in quantum corrections to GR and identifies several viable UV scenarios whose low-energy limits reproduce GR-like dynamics. These results suggest that the geometric structure of GR may arise from a fundamentally flat-space quantum field theory (QFT) involving interactions among several fields. More broadly, our approach demonstrates how automated computational…