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From conformal blocks to path integrals in the Vaidya geometry 

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Published in  Journal of High Energy Physics. 2017, vol. 1709, p. 00931  
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Open Access  SCOAP3 

Abstract  Correlators in conformal field theory are naturally organized as a sum over conformal blocks. In holographic theories, this sum must reorganize into a path integral over bulk fields and geometries. We explore how these two sums are related in the case of a point particle moving in the background of a 3d collapsing black hole. The conformal block expansion is recast as a sum over paths of the firstquantized particle moving in the bulk geometry. Offshell worldlines of the particle correspond to subdominant contributions in the Euclidean conformal block expansion, but these same operators must be included in order to correctly reproduce complex saddles in the Lorentzian theory. During thermalization, a complex saddle dominates under certain circumstances; in this case, the CFT correlator is not given by the Virasoro identity block in any channel, but can be recovered by summing heavy operators. This effectively converts the conformal block expansion in CFT from a sum over intermediate states to a sum over channels that mimics the bulk path integral.  
Keywords  AdSCFT Correspondence — Black Holes — Conformal Field Theory  
Identifiers  arXiv: 1706.02668  
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Citation (ISO format)  ANOUS, Tarek et al. From conformal blocks to path integrals in the Vaidya geometry. In: Journal of High Energy Physics, 2017, vol. 1709, p. 00931. https://archiveouverte.unige.ch/unige:97183 