On Melonic Supertensor Models

Abstract

We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large $N$ limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for $SL(2,\mathbb{R})$ wavefunctions for fermionic excitations.

37+19 pages; v2: references added. v3: typos fixed. published version

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Cited by in corpus (19)

• Jackiw-Teitelboim Gravity and Rotating Black Holes
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• Phases Of Melonic Quantum Mechanics
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Rotating Black Holes in AdS, Extremality and Chaos
• A 3d disordered superconformal fixed point
• Strongly coupled quantum phonon fluid in a solvable model
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Melonic Dominance in Subchromatic Sextic Tensor Models
• Disordered vector models: from higher spins to incipient strings
• The F-theorem in the melonic limit
• Chiral Algebras of Two-Dimensional SYK Models
• Chaos in Three-dimensional Higher Spin Gravity
• Instability of complex CFTs with operators in the principal series
• Supersymmetric Black Holes and the SJT/nSCFT${}_1$ Correspondence
• Disordered $\mathcal{N}=(2,2)$ Supersymmetric Field Theories
• The quantum $p$-spin glass model: A user manual for holographers