Free energy and defect $C$-theorem in free scalar theory

Abstract

We describe conformal defects of $p$ dimensions in a free scalar theory on a $d$-dimensional flat space as boundary conditions on the conformally flat space ${\mathbb{H}}^{p+1}\times {\mathbb{S}}^{d-p-1}$. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ${\mathbb{H}}^{p+1}$ which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on ${\mathbb{H}}^{p+1}\times {\mathbb{S}}^{d-p-1}$ between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured $C$-theorem in defect CFTs.

59 pages, 2 figures, v2: minor modifications and references added, v3: further clarification and references added, v4: published version, v5: reference added

References in corpus (18)

• Generalized Global Symmetries
• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Boundary Conformal Field Theory and a Boundary Central Charge
• The g-theorem and quantum information theory
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Line and surface defects for the free scalar field
• CFT in AdS and boundary RG flows
• Irreversibility in quantum field theories with boundaries
• Entanglement entropy of round spheres
• Boundary Entropy Can Increase Under Bulk RG Flow
• Partition function on spheres: how (not) to use zeta function regularization
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Determinants and conformal anomalies of GJMS operators on spheres
• Boundary entropy under ambient RG flow in the AdS/BCFT model
• Boundary Conformal Anomalies on Hyperbolic Spaces and Euclidean Balls
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories

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• Defect $a$-Theorem and $a$-Maximization
• Monodromy Defects from Hyperbolic Space
• Monodromy Defects in Free Field Theories
• Conformal dispersion relations for defects and boundaries
• RG flows on two-dimensional spherical defects
• Free energy and defect $C$-theorem in free fermion
• Partition functions of higher derivative conformal fields on conformally related spaces
• Defects, Rigid Holography and $C$-theorems
• Information metric on the boundary
• Flavored ABJM theory on the sphere and holographic F-functions
• Partition functions of $p$-forms from Harish-Chandra characters
• From Large to Small $\mathcal{N}=(4,4)$ Superconformal Surface Defects in Holographic 6d SCFTs