Fermions in AdS and GrossNeveu BCFT
Abstract
We study the boundary critical behavior of conformal field theories of interacting fermions in the GrossNeveu 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 GrossNeveu 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 WilsonFisher fixed point of the GrossNeveuYukawa 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 Ftheorem. We also compute some of the BCFT observables in these theories, including bulk twopoint functions of scalar and fermions, and fourpoint functions of boundary fermions.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.04268
 Bibcode:
 2021arXiv211004268G
 Keywords:

 High Energy Physics  Theory
 EPrint:
 52 pages, 2 figures, v2: minor typos corrected