$O(N)$ Models with Boundary Interactions and their Long Range Generalizations

Abstract

We study the critical properties of scalar field theories in $d+1$ dimensions with $O(N)$ invariant interactions localized on a $d$-dimensional boundary. By a combination of large $N$ and epsilon expansions, we provide evidence for the existence of non-trivial $O(N)$ BCFTs in $1<d<4$. Due to having free fields in the bulk, these models possess bulk higher-spin currents which are conserved up to terms localized on the boundary. We suggest that this should lead to a set of protected spinning operators on the boundary, and give evidence that their anomalous dimensions vanish. We also discuss the closely related long-range $O(N)$ models in $d$ dimensions, and in particular study a weakly coupled description of the $d=1$ long range $O(N)$ model near the upper critical value of the long range parameter, which is given in terms of a non-local non-linear sigma model. By combining the known perturbative descriptions, we provide some estimates of critical exponents in $d=1$.

arXiv comment64 pages, several figures. v2: minor changes, references added. v3: minor changes, journal version

References in corpus (47)

• AdS Dual of the Critical O(N) Vector Model
• Conformal Four Point Functions and the Operator Product Expansion
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Aspects of AdS/BCFT
• Is the Composite Fermion a Dirac Particle?
• The Bootstrap Program for Boundary CFT_d
• Conformality Lost
• Conformal Field Theories Near a Boundary in General Dimensions
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Unitarity and the Holographic S-Matrix
• The Higher Spin/Vector Model Duality
• Information radiation in BCFT models of black holes
• Exact Solution of a Boundary Conformal Field Theory
• Exact solution of a massless scalar field with a relevant boundary interaction
• Boundary and Interface CFTs from the Conformal Bootstrap
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• Boundary Conformal Field Theory and a Boundary Central Charge
• Energy Momentum Tensor in Conformal Field Theories Near a Boundary
• Defects in conformal field theory
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Conformal Invariance in the Long-Range Ising Model
• Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED
• A General Proof of the Quantum Null Energy Condition
• The boundary between long-range and short-range critical behavior
• Random Currents and Continuity of Ising Model's Spontaneous Magnetization
• Relations between Short Range and Long Range Ising models
• Long-range critical exponents near the short-range crossover
• Electromagnetic current correlations in reduced quantum electrodynamics
• Integrable Model of Boundary Interaction: The Paperclip
• The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
• An Analytic Approach to BCFT${}_d$
• Analytic Bootstrap for Boundary CFT
• Bootstrapping the long-range Ising model in three dimensions
• Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultra-relativistic limit of graphene
• Implications of N=1 Superconformal Symmetry for Chiral Fields
• 3d Abelian Gauge Theories at the Boundary
• Exact C=1 Boundary Conformal Field Theories
• O(N) and O(N) and O(N)
• Duality and Universal Transport in a Mixed-Dimension Electrodynamics
• Double-Trace Deformations of Conformal Correlations
• Magnetic Fields and Fractional Statistics in Boundary Conformal Field Theory
• Two-loop fermion self-energy and propagator in reduced QED${}_{3,2}$
• Superconformal Models for Graphene and Boundary Central Charges
• Composite operators near the boundary
• Non-local non-linear sigma models
• Integrable boundary interaction in 3D target space: the "pillow-brane" model

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