Yukawa conformal field theories and emergent supersymmetry

Lin Fei, Simone Giombi, Igor R. Klebanov, Grigory Tarnopolsky

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Abstract

We study conformal field theories (CFTs) withYukawa 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-∈ expansion using the Gross-Neveu-Yukawa model, and the first few terms in the 2 + ∈ expansion using the four-fermion interaction. We then apply Padé approximants to produce estimates in d = 3. For N = 1, which corresponds to one two-component Majorana fermion, it has been suggested that the Yukawa theory flows to an N = 1 supersymmetric CFT. We provide new evidence that the 4 - ∈ 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 two-component Dirac fermion, this theory has an emergent supersymmetry with four supercharges, and we provide new evidence for this.

Original languageEnglish (US)
Article number12C105
JournalProgress of Theoretical and Experimental Physics
Volume2016
Issue number12
DOIs
StatePublished - Dec 2016

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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