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.

arXiv comment52 pages, 2 figures, v2: minor typos corrected

References in corpus (51)

• Conformal Four Point Functions and the Operator Product Expansion
• Quantum Field Theory in the Large N Limit: a review
• Chern-Simons Theory with Vector Fermion Matter
• The Bootstrap Program for Boundary CFT_d
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• The Theory of Boundary Critical Phenomena
• Level/rank Duality and Chern-Simons-Matter Theories
• Conformal Field Theories Near a Boundary in General Dimensions
• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
• Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section
• Spinors and the AdS/CFT correspondence
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Conformal Field Theory Correlators from Classical Field Theory on Anti-de Sitter Space II. Vector and Spinor Fields
• The S-matrix Bootstrap I: QFT in AdS
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• A Constraint on Defect and Boundary Renormalization Group Flows
• Boundary Conformal Field Theory and a Boundary Central Charge
• Energy Momentum Tensor in Conformal Field Theories Near a Boundary
• Partition functions and double-trace deformations in AdS/CFT
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Towards a $C$-theorem in defect CFT
• On the origin of supergravity boundary terms in the AdS/CFT correspondence
• Displacement Operators and Constraints on Boundary Central Charges
• Computation of $\beta (g_c)$ at O(1/N^2) in the O(N) Gross Neveu Model in Arbitrary Dimensions
• Conformal field theories in anti-de Sitter space
• Boundary terms in the AdS/CFT correspondence for spinor fields
• CFT in AdS and boundary RG flows
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Anomalies, entropy and boundaries
• Spectral invariants for the Dirac equation on the d-Ball with various boundary conditions
• On Marginal Operators in Boundary Conformal Field Theory
• Spinor Exchange in AdS_{d+1}
• Aspects of CFTs on Real Projective Space
• Double-trace deformations, holography and the c-conjecture
• Spinor Parallel Propagator and Green's Function in Maximally Symmetric Spaces
• Supersymmetric Multi-trace Boundary Conditions in AdS
• Flowing Between Fermionic Fixed Points
• Towards Bootstrapping RG flows: Sine-Gordon in AdS
• Superconformal Models for Graphene and Boundary Central Charges
• Mellin Amplitudes for Fermionic Conformal Correlators
• Fermions in Geodesic Witten Diagrams
• Hamiltonian truncation in Anti-de Sitter spacetime
• Yukawa CFTs and Emergent Supersymmetry
• Free energy and defect $C$-theorem in free fermion
• Gravitino Propagator in anti de Sitter space
• Boundary Conformal Anomalies on Hyperbolic Spaces and Euclidean Balls
• Supersymmetric Field Theories on AdS_p x S^q
• Determinant and Weyl anomaly of Dirac operator: a holographic derivation

Cited by in corpus (17)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Conformal Surface Defects in Maxwell Theory are Trivial
• 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