2016/07/18 by Lin Fei, Simone Giombi, Fei, Lin +5 · 6 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.1607.05316
openalex publication_date 2016/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-ε expansion using the Gross-Neveu-Yukawa model, and the first few terms in the 2+ε 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-ε 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.