CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
Klebanov and Grigory Tarnopolsky,Yukawa CFTs and Emergent Supersymmetry, [arXiv:1607.05316pdf], [Inspire]
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
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 ${\cal N}=1$ 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.
citation-role summary
background 2
citation-polarity summary
fields
hep-th 4verdicts
UNVERDICTED 4roles
background 2polarities
background 2representative citing papers
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
Exact infrared solutions for surface criticalities in the Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent structures linked to a defect version of the CFT distance conjecture.
The work constructs an equivalence class of 3D lattice models realizing single Weyl fermions through symmetry-protected topological states and controlled symmetry breaking, linking them to gapless phases in superconductors and superfluids.
citing papers explorer
-
Moduli Spaces in CFT: Large Charge Operators
CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
-
Local CFTs extremise $F$
Local CFTs lie at the extrema of the sphere free energy tilde F for nonlocal CFT lines, and maximize it when unitary.
-
Extraordinary Surface Criticalities for Interacting Fermions
Exact infrared solutions for surface criticalities in the Gross-Neveu-Yukawa model encode fermionic anomalies in surface dynamics and reveal emergent structures linked to a defect version of the CFT distance conjecture.
-
Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions
The work constructs an equivalence class of 3D lattice models realizing single Weyl fermions through symmetry-protected topological states and controlled symmetry breaking, linking them to gapless phases in superconductors and superfluids.