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.

Conformal surface defects in Maxwell theory are trivial

“…The earliest example we found was from 35 years ago [15], where a free scalar field in three dimensions interacts via a classically marginal φ 4 coupling on a two dimensional boundary. More recent work utilizing and large N expansions to study boundary interactions includes [16][17][18][19][20][21].…”

Fermions in boundary conformal field theory: crossing symmetry and E-expansion

“…To our knowledge, relatively little theoretical work has been done on critical fermionic systems with boundaries. While a recent tour-de-force calculation [20] computes critical exponents in the Yukawa model at fourth order in the epsilon expansion in the infinite system, the state of the art in the presence of a boundary is O( ) [21]. Refs.…”

“…Refs. [21,22] consider also the large N f limit. On the experimental side, the associated critical exponents have not yet been measured in the infinite system nor in the presence of a boundary, yet much promising work has been done to engineer graphene and graphene like systems which undergo this type of chiral symmetry breaking phase transition (see e.g.…”

Interacting conformal scalar in a wedge

“…In this section, we study the bulk-wedge two-point functions of scalar operators, and how they can be found from the Dyson-Schwinger (DS) equations up to O( ) with a quartic interaction in the bulk in d = 4 − , or a quartic boundary interaction in d = 3 − . This approach has been used in [63,64] in the context of a single boundary with a bulk interaction in d = 4 − . In a WCFT there are four OPE's in play: two for each boundary, which allow us to express bulk operators in terms of the boundary operators, and two more which express the boundary operators on the wall or the ramp in terms of edge operators.…”