Using worldline formalism and geometric quantization, the partition function for 3D gravity with matter on thermal AdS3 is computed via equivariant localization, reproducing the Wilson spool and conjecturing the all-orders result.
A view of the bulk from the worldline
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abstract
A new method to compute correlation functions in AdS$_{d+1}$ in general dimension is introduced, considering a particle quantised in the worldline formalism of quantum field theory, coupled to bulk fields, in particular gravity, quantised in the standard manner. This gives a systematic two-parameter perturbative expansion organised by small parameters $G_N$ and the inverse mass of the particle, complementary to the usual Witten diagram expansion. This connects closely to CFT language, with the geodesic Witten diagram representation of global conformal blocks emerging naturally, and for two dimensions gives a bulk representation of the Virasoro block, with a systematic method for computing quantum corrections. The global conformal block and other contributions are shown to exponentiate in correlation functions in any dimension, corresponding to pieces of Witten diagrams at arbitrary loop order.
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What's the Matter with 3D Gravity?
Using worldline formalism and geometric quantization, the partition function for 3D gravity with matter on thermal AdS3 is computed via equivariant localization, reproducing the Wilson spool and conjecturing the all-orders result.