A bstract 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,more »
CFT in AdS and boundary RG flows
A bstract Using the fact that flat space with a boundary is related by a Weyl transformation to antide Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O ( N ) model in general dimension d , as well as its perturbative descriptions in the epsilonexpansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, more »
 Award ID(s):
 1914860
 Publication Date:
 NSFPAR ID:
 10206131
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2020
 Issue:
 11
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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