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Fermions in AdS and Gross-Neveu BCFT

Author(s): Giombi, Simone; Helfenberger, Elizabeth; Khanchandani, Himanshu

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Abstract: <jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We study the boundary critical behavior of conformal field theories of interacting fermions in the Gross-Neveu universality class. By a Weyl transformation, the problem can be studied by placing the CFT in an anti de Sitter space background. After reviewing some aspects of free fermion theories in AdS, we use both large <jats:italic>N</jats:italic> methods and the epsilon expansion near 2 and 4 dimensions to study the conformal boundary conditions in the Gross-Neveu CFT. At large <jats:italic>N</jats:italic> and general dimension <jats:italic>d</jats:italic>, we find three distinct boundary conformal phases. Near four dimensions, where the CFT is described by the Wilson-Fisher fixed point of the Gross-Neveu-Yukawa model, two of these phases correspond respectively to the choice of Neumann or Dirichlet boundary condition on the scalar field, while the third one corresponds to the case where the bulk scalar field acquires a classical expectation value. One may flow between these boundary critical points by suitable relevant boundary deformations. We compute the AdS free energy on each of them, and verify that its value is consistent with the boundary version of the F-theorem. We also compute some of the BCFT observables in these theories, including bulk two-point functions of scalar and fermions, and four-point functions of boundary fermions.</jats:p>
Publication Date: 4-Jul-2022
Electronic Publication Date: 4-Jul-2022
Citation: Giombi, Simone, Helfenberger, Elizabeth, Khanchandani, Himanshu. (2022). Fermions in AdS and Gross-Neveu BCFT. Journal of High Energy Physics, 2022 (7), 10.1007/jhep07(2022)018
DOI: doi:10.1007/jhep07(2022)018
EISSN: 1029-8479
Keywords: Boundary Quantum Field Theory, Scale and Conformal Symmetries
Language: en
Type of Material: Journal Article
Journal/Proceeding Title: Journal of High Energy Physics
Version: Final published version. This is an open access article.

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