Fermions in AdS and Gross-Neveu BCFT

Abstract

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 $N$ methods and the epsilon expansion near 2 and 4 dimensions to study the conformal boundary conditions in the Gross-Neveu CFT. At large $N$ and general dimension $d$, 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.

52 pages, 2 figures, v2: minor typos corrected

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• Gravitino Propagator in anti de Sitter space
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• Interacting conformal scalar in a wedge
• Exploring Confinement in Anti-de Sitter Space
• RG Flows and Stability in Defect Field Theories
• Phases of theories with fermions in AdS
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Surface quantum critical phenomena in disordered Dirac semimetals
• Boundary and defect criticality in topological insulators and superconductors
• Boundary criticality for the Gross-Neveu-Yukawa models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Disclinations, dislocations, and emanant flux at Dirac criticality
• Partition functions for $U(1)$ vectors and phases of scalar QED in AdS
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Boundary critical behavior of the Gross-Neveu-Yukawa model