2PI effective action for the SYK model and tensor field theories

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.

38 pages, 11 figures; v2: added interpretation of the subleading terms in the GW model, together with some references, one figure, and an appendix

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Cited by in corpus (37)

• Jackiw-Teitelboim Gravity and Rotating Black Holes
• Thouless time for mass-deformed SYK
• Phases Of Melonic Quantum Mechanics
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Line of fixed points in a bosonic tensor model
• Functional renormalization group and 2PI effective action formalism
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Rotating Black Holes in AdS, Extremality and Chaos
• On Melonic Supertensor Models
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• Melonic Dominance in Subchromatic Sextic Tensor Models
• The F-theorem in the melonic limit
• Hints of unitarity at large $N$ in the $O(N{)}^3$ tensor field theory
• Chaos in Three-dimensional Higher Spin Gravity
• Remarks on a melonic field theory with cubic interaction
• Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Near Conformal Perturbation Theory in SYK Type Models
• Instability of complex CFTs with operators in the principal series
• Complete Solution of a Gauged Tensor Model
• Diagrammatic proof of the large $N$ melonic dominance in the SYK model
• Explicit holography for vector models at finite $N$, volume and temperature
• A Solvable Tensor Field Theory
• True SYK or (con)sequences
• Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions
• Sextic tensor field theories in rank $3$ and $5$
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Tensor Field Theories: Renormalization and Random Geometry
• A simple model for Hawking radiation
• Multiple scaling limits of $\mathrm{U}(N{)}^2\times \mathrm{O}(D)$ multi-matrix models
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Time-translation invariance symmetry breaking hidden by finite-scale singularities
• The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group