Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions

Abstract

Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely the smallest colored tensor model due to Gurau and Witten that exhibits non-linearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of $N$, exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the gory details will appear in a companion paper.

5 + epsilon pages, 1 figure; v2: minor comments and a reference added

References in corpus (10)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• More on Supersymmetric and 2d Analogs of the SYK Model
• Invitation to Random Tensors
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Contrasting SYK-like Models
• Towards a Finite-$N$ Hologram
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Complete Solution of a Gauged Tensor Model

Cited by in corpus (14)

• Jackiw-Teitelboim Gravity and Rotating Black Holes
• 2PI effective action for the SYK model and tensor field theories
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• Phases Of Melonic Quantum Mechanics
• SYK-like tensor quantum mechanics with $\mathrm{Sp}(N)$ symmetry
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Spectrum of Majorana Quantum Mechanics with $O(4{)}^3$ Symmetry
• Majorana Fermion Quantum Mechanics for Higher Rank Tensors
• On Melonic Supertensor Models
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• Quantum resonant systems, integrable and chaotic
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Complete Solution of a Gauged Tensor Model
• A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory