Tensorial Gross-Neveu models

Abstract

We define and study various tensorial generalizations of the Gross-Neveu model in two dimensions, that is, models with four-fermion interactions and $G^3$ symmetry, where we take either $G=U(N)$ or $G=O(N)$. Such models can also be viewed as two-dimensional generalizations of the Sachdev-Ye-Kitaev model, or more precisely of its tensorial counterpart introduced by Klebanov and Tarnopolsky, which is in part our motivation for studying them. Using the Schwinger-Dyson equations at large-$N$, we discuss the phenomenon of dynamical mass generation and possible combinations of couplings to avoid it. For the case $G=U(N)$, we introduce an intermediate field representation and perform a stability analysis of the vacua. It turns out that the only apparently viable combination of couplings that avoids mass generation corresponds to an unstable vacuum. The stable vacuum breaks $U(N{)}^3$ invariance, in contradiction with the Coleman-Mermin-Wagner theorem, but this is an artifact of the large-$N$ expansion, similar to the breaking of continuous chiral symmetry in the chiral Gross-Neveu model.

45 pages, 9 figures; v2: new discussion of beta function and IR fixed point in d=2-ε(section 3.2 and appendix C), minor corrections, and references added; v3: minor corrections (mainly concerning figures 3 and 4)

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• More on Supersymmetric and 2d Analogs of the SYK Model
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• The 1/N expansion of colored tensor models
• The complete $1/N$ expansion of a SYK--like tensor model
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• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Lectures on Yangian Symmetry
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Cited by in corpus (30)

• An introduction to the SYK model
• 2PI effective action for the SYK model and tensor field theories
• The $1/N$ expansion of the symmetric traceless and the antisymmetric tensor models in rank three
• Phases Of Melonic Quantum Mechanics
• A Complex Fermionic Tensor Model in $d$ Dimensions
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• Line of fixed points in a bosonic tensor model
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry
• Combinatorial aspects of the Sachdev-Ye-Kitaev model
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Melonic Dominance in Subchromatic Sextic Tensor Models
• The tri-fundamental quartic model
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• Reliability of the local truncations for the random tensor models renormalization group flow
• Hints of unitarity at large $N$ in the $O(N{)}^3$ tensor field theory
• Remarks on a melonic field theory with cubic interaction
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Spectrum of a Gross-Neveu Yukawa model with flavor disorder in $d=3$
• Diagrammatic proof of the large $N$ melonic dominance in the SYK model
• A Renormalizable SYK-type Tensor Field Theory
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Sextic tensor model in rank $3$ at next-to-leading order
• Sextic tensor field theories in rank $3$ and $5$
• Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Tensor Field Theories: Renormalization and Random Geometry
• Multiple scaling limits of $\mathrm{U}(N{)}^2\times \mathrm{O}(D)$ multi-matrix models
• Melonic large $N$ limit of $5$-index irreducible random tensors