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2PI effective action for the SYK model and tensor field theories
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abstract
We discuss the two-particle irreducible (2PI) effective action for the SYK model and for tensor field theories. For the SYK model the 2PI effective action reproduces the bilocal reformulation of the model without using replicas. In general tensor field theories the 2PI formalism is the only way to obtain a bilocal reformulation of the theory, and as such is a precious instrument for the identification of soft modes and for possible holographic interpretations. We compute the 2PI action for several models, and push it up to fourth order in the $1/N$ expansion for the model proposed by Witten in arXiv:1610.09758, uncovering a one-loop structure in terms of an auxiliary bilocal action.
Forward citations
Cited by 2 Pith papers
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$F$-extremization determines certain large-$N$ CFTs
Melonic large-N CFTs are exactly the conformal mean field theories that extremize the universal part of the sphere free energy under linear IR marginality constraints.
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Notes on Tensor Models and Tensor Field Theories
Lecture notes introducing the 1/N expansion and melonic limit of tensor models, which yield new conformal field theories.
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