Comments on epsilon expansion of the O(N) model with boundary
Tatsuma Nishioka, Yoshitaka Okuyama, Soichiro Shimamori
Abstract
A bstract The O( N ) vector model in the presence of a boundary has a non-trivial fixed point in (4 − ϵ ) dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is investigated at the leading order in the ϵ -expansion by diagrammatic and axiomatic approaches. In the latter, we extend the framework of Rychkov and Tan for the bulk theory to the case with a boundary and calculate the conformal dimensions of boundary composite operators with attention to the analyticity of correlation functions. In both approaches, we obtain consistent results.
Topics & Concepts
Boundary conformal field theoryPhysicsBoundary (topology)Conformal mapDiagrammatic reasoningConformal field theoryBoundary value problemMathematical physicsAxiomSpectrum (functional analysis)Field (mathematics)Mathematical analysisMixed boundary conditionPure mathematicsRobin boundary conditionGeometryQuantum mechanicsMathematicsPhilosophyLinguisticsAlgebraic structures and combinatorial modelsTheoretical and Computational PhysicsBlack Holes and Theoretical Physics