Emergent Supersymmetry at Large $N$

Abstract

We search for infrared fixed points of Gross-Neveu Yukawa models with matrix degrees of freedom in $d=4-\epsilon$. We consider three models -- a model with $SU(N)$ symmetry in which the scalar and fermionic fields both transform in the adjoint representation, a model with $SO(N)$ symmetry in which the scalar and fermion fields both transform as real symmetric-traceless matrices, and a model with $SO(N)$ symmetry in which the scalar field transforms as a real symmetric-traceless matrix, while the fermion transforms in the adjoint representation. These models differ at finite $N$, but their large-$N$ limits are perturbatively equivalent. The first two models contain a supersymmetric fixed point for all $N$, which is attractive to all classically-marginal deformations for $N$ sufficiently large. The third model possesses a stable fixed point that, although non-supersymmetric, gives rise to many correlation functions that are identical to those of a supersymmetric fixed point when $N$ is sufficiently large. We also find several non-supersymmetric fixed points at finite and large-$N$. Planar diagrams dominate the large-$N$ limit of these fixed points, which suggests the possibility of a stringy holographic dual description.

80 pages, 19 figures. v2: fixed typos and added references; v3: accepted for publication in JHEP

References in corpus (19)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Interactions and phase transitions on graphene's honeycomb lattice
• Theory of interacting electrons on the honeycomb lattice
• Volume independence in large Nc QCD-like gauge theories
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Emergence of supersymmetry at a critical point of a lattice model
• (In)validity of large N orientifold equivalence
• Large N Field Theory and AdS Tachyons
• Four loop renormalization of the Gross-Neveu model
• The Gross-Neveu-Yukawa Archipelago
• On the Conformal Field Theory Duals of type IIA AdS_4 Flux Compactifications
• Asymptotic safety with Majorana fermions and new large N equivalences
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Four loop MSbar mass anomalous dimension in the Gross-Neveu model
• Pure Supersymmetric AdS and the Swampland
• A Non-Supersymmetric Large-N 3D CFT And Its Gravity Dual
• Aspects of AdS flux vacua with integer conformal dimensions
• Holographic Perspectives On Models Of Moduli Stabilization In M-Theory
• The fate of non-supersymmetric Gross-Neveu-Yukawa fixed point in two dimensions