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Geometric construction of D-branes in WZW models
High Energy Physics - Theory · Submitted 25 Apr 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes.
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The abstract, sentence by sentence
The geometric description of D-branes in WZW models is pushed forward. Our starting point is a gluing condition\, $J_{+}=FJ_-$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. The equivalence of boundary and gluing conditions of this type is studied in detail. The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes. The isometry $F$ need not be a Lie algebra automorphism nor constantly defined over the brane. This approach, when applied to isometries of the form $F=R$ with $R$ a constant Lie algebra automorphism, validates metrically degenerate $R$-twined conjugacy classes as D-branes. It also shows that no D-branes exist in semisimple WZW models for constant\, $F=-R$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The geometric description of D-branes in WZW models is pushed forward. | contribution 0.93 | 0.79 | 0.09 | asserted 0.96 |
| s1 | Our starting point is a gluing condition\, $J_{+}=FJ_-$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. | method 0.92 | 0.48 | 0.06 | asserted 1.00 |
| s2 | The equivalence of boundary and gluing conditions of this type is studied in detail. | contribution 0.91 | 0.85 | 0.06 | asserted 0.94 |
| s3 | The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes. | method 0.49 | 0.90 | 0.20 | asserted 1.00 |
| s4 | The isometry $F$ need not be a Lie algebra automorphism nor constantly defined over the brane. | result 0.98 | 0.81 | 0.14 | asserted 0.63 |
| s5 | This approach, when applied to isometries of the form $F=R$ with $R$ a constant Lie algebra automorphism, validates metrically degenerate $R$-twined conjugacy classes as D-branes. | result 0.96 | 0.83 | 0.18 | asserted 1.00 |
| s6 | It also shows that no D-branes exist in semisimple WZW models for constant\, $F=-R$. | result 1.00 | 0.90 | 0.12 | asserted 1.00 |
What was examined, and what was not
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The paper
Original abstract
The geometric description of D-branes in WZW models is pushed forward. Our starting point is a gluing condition\, $J_{+}=FJ_-$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. The equivalence of boundary and gluing conditions of this type is studied in detail. The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes. The isometry $F$ need not be a Lie algebra automorphism nor constantly defined over the brane. This approach, when applied to isometries of the form $F=R$ with $R$ a constant Lie algebra automorphism, validates metrically degenerate $R$-twined conjugacy classes as D-branes. It also shows that no D-branes exist in semisimple WZW models for constant\, $F=-R$.
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How the literature uses it
1 arXiv paper cite this in 13 sentences
Papers citing it · 10 sentences without a confident label
Cites it as background 1 paper
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[ref] for details and Sections 4 and 5 for examples.
D-branes with Lorentzian signature in the Nappi-Witten model · Characterization of D-branes in WZW models · 0.82
What it cites · 41 sentences without a confident label
Builds on 4 papers
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They are met by $F$ any constant $$-preserving Lie algebra automorphism $R$, so the well known result [ref] that the $R$-twined conjugacy classes of the group $G$ are D-branes extends to metrically degenerate classes.
A note on D-branes in group manifolds: flux quantisation and D0-charge · Conclusion · 1.00
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They are met by $F$ any constant $$-preserving Lie algebra automorphism $R$, so the well known result [ref] that the $R$-twined conjugacy classes of the group $G$ are D-branes extends to metrically degenerate classes.
D-branes in the WZW model · Conclusion · 1.00
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They are met by $F$ any constant $$-preserving Lie algebra automorphism $R$, so the well known result [ref] that the $R$-twined conjugacy classes of the group $G$ are D-branes extends to metrically degenerate classes.
D-branes in an AdS_3 background · Conclusion · 1.00
Uses the method or tool of 1 paper
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To do this [ref] , it is enough to use for the chiral currents their expressions [equation] in terms of the string coordinates $X^$ and the left and right-invariant vielbeins $e^ A_$ and $e̅^ A_$.
D-branes in group manifolds · Gluing conditions for chiral currents · 0.97
Cites as background 19 papers
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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.
Boundary Spectra in Superspace Sigma-Models · Introduction · 0.99
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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.
Boundary Correlators in Supergroup WZNW Models · Introduction · 0.99
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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.
Inner brane: A D3-brane in the Nappi-Witten model from an inner group automorphism · Introduction · 0.99
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