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arXiv:2502.19547 · Journal of High Energy Physics

Codimension one defects in free scalar field theory

Seolhwa Kim, Per Kraus, Zhengdi Sun

Published Jun 6, 2025• 1 citation
arXivHTMLPDF

Abstract

A bstract We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as special cases. Our analysis is based on the interplay between two complementary descriptions, the first involving matching conditions imposed on fields and their derivatives across the defect, and the second on the resummation of perturbation theory in terms of renormalized defect couplings. Using either description as appropriate we compute a variety of observables: correlators of fields in the presence of such defects; the defect anomalous dimension; multiple defects and their fusion; canonical quantization and instabilities; ring shaped defects with application to the g-theorem and the entanglement entropy of accelerating defects; defects on the torus and Cardy formulas for the asymptotic density of states of the defect Hilbert space; and quenches produced by spacelike defects. The simplicity of the model allows for explicit computation of all these quantities, and provides a starting point for more complicated theories involving interactions.

DOI
10.1007/jhep06(2025)065

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A bstract We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as special cases. Our analysis is based on the interplay between two complementary descriptions, the first involving matching conditions imposed on fields and their derivatives across the defect, and the second on the resummation of perturbation theory in terms of renormalized defect couplings. Using either description as appropriate we compute a variety of observables: correlators of fields in the presence of such defects; the defect anomalous dimension; multiple defects and their fusion; canonical quantization and instabilities; ring shaped defects with application to the g-theorem and the entanglement entropy of accelerating defects; defects on the torus and Cardy formulas for the asymptotic density of states of the defect Hilbert space; and quenches produced by spacelike defects. The simplicity of the model allows for explicit computation of all these quantities, and provides a starting point for more complicated theories involving interactions.
A bstract Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible quadratic defects, we explore interacting setups. These are realized by coupling the bulk free scalar to lower-dimensional theories, including the unitary family of minimal models M(m,m+1) \mathcal{M}\left(m,m+1\right) M(m,m+1) M m m + 1 . Another example involves coupling to a two-dimensional free scalar field, from which we construct surface defects for the bulk dimensions three and five. Additionally, we consider monodromy defects associated with a global U(1) flavour symmetry. In these theories, we study both self-defect interactions and couplings to Minimal Models, finding new IR defect fixed points. For all our examples, we provide results for correlation functions, such as those involving the bulk stress tensor and the displacement operator, and for the defect central charges.
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A bstract We study quenched disorder localized on a p -dimensional subspacetime in a d -dimensional conformal field theory. Motivated by the logarithmic behavior often associated with disorder, we introduce a defect setup in which bulk local operators transform in ordinary conformal representations, while defect local operators assemble into logarithmic multiplets. We refer to such objects as logarithmic defects and investigate their model-independent properties dictated solely by conformal symmetry and its representation theory, including correlation functions, logarithmic defect operator expansions, and conformal blocks. As a concrete example, we analyze the free scalar theory with a generalized pinning defect subject to random coupling fluctuations, and we identify a half-line of fixed points describing the corresponding logarithmic conformal defects. Along the way, we propose a candidate monotone governing defect renormalization group flows induced by subdimensional disorder, and demonstrate its consistency with such flows in the free theory across various dimensions. We further comment on generalizations and outline a broader program for bootstrapping logarithmic defects.
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Abstract Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension d ≥ 5 with a conformally-invariant spatial boundary (BCFTs) or 4-dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing Wess-Zumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT’s Weyl tensor. For a co-dimension one boundary or defect (i.e. d = 5), we reproduce the 9 parity-even terms found by Astaneh and Solodukhin, and we discover 3 parity-odd terms. For larger co-dimension, we find 23 parity-even terms and 6 parity-odd terms. The coefficient of each term defines a “central charge” that characterizes the BCFT or DCFT. We show how several of the parity-even central charges enter physical observables, namely the displacement operator two-point function, the stress-tensor one-point function, and the universal part of the entanglement entropy. We compute several parity-even central charges in tractable examples: monodromy and conical defects of free, massless scalars and Dirac fermions in d = 6; probe branes in Anti-de Sitter (AdS) space dual to defects in CFTs with d ≥ 6; and Takayanagi’s AdS/BCFT with d = 5. We demonstrate that several of our examples obey the boundary/defect a-theorem, as expected.
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