Operator expansions, layer susceptibility and two-point functions in BCFT

Abstract

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function $⟨{\varphi }_i{\varphi }^i⟩$ of the O(N) model at the extraordinary transition in 4-$\epsilon$ dimensional semi-infinite space to order $O(\epsilon )$. The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order $O({\epsilon }^2)$. These agree with the known results both in $\epsilon$ and large-N expansions.

arXiv comment34 pages, 1 figure, v2: minor improvements

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Cited by in corpus (17)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The critical O(N) CFT: Methods and conformal data
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• A plane defect in the 3d O$(N)$ model
• On Analytic Bootstrap for Interface and Boundary CFT
• Conformal Bootstrap near the edge
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Fusion of conformal defects in four dimensions
• Boundary conformal field theory at the extraordinary transition: The layer susceptibility to $O(\epsilon )$
• Why boundary conditions do not generally determine the universality class for boundary critical behavior
• The ordinary surface universality class of the three-dimensional O($N$) model
• Boundary operator expansion and extraordinary phase transition in the tricritical O(N) model
• Spontaneous symmetry breaking in free theories with boundary potentials
• Boundary Conformal Field Theory at Large Charge
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Boundary conformal field theory, holography and bulk locality