Yukawa CFTs and Emergent Supersymmetry

Abstract

We study conformal field theories with Yukawa interactions in dimensions between 2 and 4; they provide UV completions of the Nambu-Jona-Lasinio and Gross-Neveu models which have four-fermion interactions. We compute the sphere free energy and certain operator scaling dimensions using dimensional continuation. In the Gross-Neveu CFT with $N$ fermion degrees of freedom we obtain the first few terms in the $4-\epsilon$ expansion using the Gross-Neveu-Yukawa model, and the first few terms in the $2+\epsilon$ expansion using the four-fermion interaction. We then apply Pade approximants to produce estimates in $d=3$. For $N=1$, which corresponds to one 2-component Majorana fermion, it has been suggested that the Yukawa theory flows to a $\mathcal{N}=1$ supersymmetric CFT. We provide new evidence that the $4-\epsilon$ expansion of the $N=1$ Gross-Neveu-Yukawa model respects the supersymmetry. Our extrapolations to $d=3$ appear to be in good agreement with the available results obtained using the numerical conformal bootstrap. Continuation of this CFT to $d=2$ provides evidence that the Yukawa theory flows to the tri-critical Ising model. We apply a similar approach to calculate the sphere free energy and operator scaling dimensions in the Nambu-Jona-Lasinio-Yukawa model, which has an additional $U(1)$ global symmetry. For $N=2$, which corresponds to one 2-component Dirac fermion, this theory has an emergent supersymmetry with 4 supercharges, and we provide new evidence for this.

arXiv comment45 pages, 7 figures. v3: version published in PTEP

References in corpus (22)

• Towards a derivation of holographic entanglement entropy
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• On the RG running of the entanglement entropy of a circle
• Seeing a c-theorem with holography
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Emergence of supersymmetry at a critical point of a lattice model
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• Partition functions and double-trace deformations in AdS/CFT
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Bootstrapping SCFTs with Four Supercharges
• Quantum superconducting criticality in graphene and topological insulators
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Superconducting quantum criticality of topological surface states at three loops
• Generalized $F$-Theorem and the $\epsilon$ Expansion
• Optical conductivity of topological surface states with emergent supersymmetry
• On RG Flow of tau_{RR} for Supersymmetric Field Theories in Three-Dimensions
• Dynamical Symmetry Breaking in QED_3 from the Wilson RG Point of View
• The (2+1)-dimensional Gross-Neveu model with a U(1) chiral symmetry at non-zero temperature
• The Nambu-Jona-Lasinio Model at O(1/N^2)
• The Beta-Function of the Chiral Gross Neveu Model at O(1/N^2)
• Dimensional renormalization of Yukawa theories wia Wilsonian methods

Cited by in corpus (17)

• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Decoding a Three-Dimensional Conformal Manifold
• Duality and bosonization of (2+1)d Majorana fermions
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Scalar CFTs and Their Large N Limits
• Fermions in AdS and Gross-Neveu BCFT
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• Correction exponents in the Gross - Neveu - Yukawa model at $1/N^2$
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Anti-brane uplift instability from goldstino condensation
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• Is there supersymmetric Lee-Yang fixed point in three dimensions?
• Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model
• On Large N Expansion of the Sphere Free Energy
• Topological Quantum Critical Points in Strong Coupling limits: Global Symmetries and Strongly Interacting Majorana Fermions
• Loop calculations for models of graphene
• Generalized Gross-Neveu Universality Class with Non-Abelian Symmetry