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arXiv · 2607.01319

What's the Matter with 3D Gravity?

Robert Bourne·Jackson R. Fliss·Bob Knighton
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Abstract

We revisit the problem of minimally coupling matter to Einstein gravity in three dimensions with negative cosmological constant. By working in the worldline formalism, we construct a classical phase space on an initial time surface $\Sigma$, which we quantize using geometric quantization. States in the Hilbert space correspond to Virasoro conformal blocks with operators of conformal weight $h<c/24$. As an application of our formalism, we compute the partition function on thermal $\text{AdS}_3$ through equivariant localization. Our answer reproduces the AdS$_3$ Wilson spool and agrees with the known one-loop result. It further serves as a conjecture for the value of the path integral of gravity minimally coupled to a massive scalar field in thermal $\text{AdS}_3$ to all orders in $G_N$.

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Robert Bourne, Jackson R. Fliss, Bob Knighton. 2026-07-01. What's the Matter with 3D Gravity?. https://arxiv.org/abs/2607.01319

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