Symmetry breaking boundaries I. General theory

C. Schweigert; J. Fuchs

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Symmetry breaking boundaries I. General theory

J. Fuchs, C. Schweigert

High Energy Physics - Theory · Submitted 18 Feb 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Integrality of the annulus coefficients is proven in full generality.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.04 · mentions code or data availability 0.02.

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We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group. We explicitly construct the boundary states and reflection coefficients as well as the annulus amplitudes. Integrality of the annulus coefficients is proven in full generality.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study conformally invariant boundary conditions that break part of the bulk symmetries.	contribution 0.81	0.88	0.07	asserted 0.89
s1	A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.	contribution 0.92	0.90	0.15	asserted 1.00
s2	We explicitly construct the boundary states and reflection coefficients as well as the annulus amplitudes.	contribution 0.90	0.95	0.13	asserted 1.00
s3	Integrality of the annulus coefficients is proven in full generality.	result 0.99	0.92	0.32	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group. We explicitly construct the boundary states and reflection coefficients as well as the annulus amplitudes. Integrality of the annulus coefficients is proven in full generality.

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References

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The Bootstrap of Points and Lines
hep-th 2025-06 accept novelty 8.0 of 10

A mixed-correlator bootstrap for 2D boundary CFTs produces new rigorous bounds on boundary entropy, bulk-to-boundary OPE coefficients, and gap spectra, tested on Ising and free boson and applied to su(2)_2 WZW.
On the Ising/tricritical-Ising interface: From ${W}_3$ symmetry to Rydberg atoms
hep-th 2026-05 unverdicted novelty 7.0 of 10

A new TIM/Ising conformal interface is identified with emergent W3 symmetry, yielding defect spectrum predictions for Rydberg atom experiments.
Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
hep-th 2026-05 unverdicted novelty 7.0 of 10

Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
hep-th 2025-11 unverdicted novelty 6.0 of 10

Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Reflection and Transmission for Conformal Defects
hep-th 2006-11 conditional novelty 6.0 of 10

Two quantities defined from stress-tensor expectation values serve as computable measures of reflection and transmission at conformal defect lines, with exact values obtained for the Ising model and several minimal-mo...

Show 3 more citing papers

Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
hep-th 2025-08 unverdicted novelty 5.0 of 10

Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
hep-th 2024-12 conditional novelty 5.0 of 10

New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.
Open Strings
hep-th 2002-04 accept novelty 2.0 of 10

A review showing how the torus, Klein bottle, annulus and Möbius amplitudes plus tadpole cancellation determine open-string spectra and gauge groups, bridging world-sheet orientifolds to D-brane and O-plane geometry.

How the literature uses it

11 arXiv papers cite this in 16 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 9 sentences without a confident label

Cites it as background 5 papers

Among them, the geometric approach [ref] , that regards D-branes as spacetime's submanifolds on which the string worldsheet boundary may be embedded, and the algebraic approach [ref] , that makes use of boundary conformal field theory.

Geometric construction of D-branes in WZW models · Introduction · 0.99
When the CFT is defined on an open manifold, it has been known that many interesting conformal boundary conditions will (partially) break the global symmetry [ref] .

Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking · Symmetry breaking conformal boundary or interface · 0.93
These extended boundary conditions are called symmetry-breaking branes or symmetry-breaking boundary conditions in high energy physics [ref] and new boundary conditions in condensed matter or statistical mechanical physics [ref] (we note the textbook [ref] for reference).

Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant · Anomalous theory and massive flow: spontaneous symmetry breaking versus breaking of extended symmetry · 0.81

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