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 − ε. 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.