REVIEW
Nonlinear Realization and Weyl Scale Invariant p=2 Brane
High Energy Physics - Theory · Submitted 18 Feb 2006 · 2 references
Pith's reading: A Weyl invariant p=2 brane action and its dual D2 brane Born-Infeld form are constructed via nonlinear realization of the super-Weyl group broken to W(1,2).
The paper
The paper claims
A Weyl invariant p=2 brane action and its dual D2 brane Born-Infeld form are constructed via nonlinear realization of the super-Weyl group broken to W(1,2).
The reading
The main result is a Weyl invariant action for the p=2 brane, Eq. (27), which is the standard conformal membrane action built from fields defined through the coset. A dual form, Eq. (43), is a supersymmetric Born-Infeld type action for a D2 brane. The paper then adds localized matter fields on the brane, introducing a Weyl gauge field as a compensating field to keep the matter couplings invariant under local scale transformations.
The calculation follows the approach of earlier papers, mainly by Clark, Nitta and ter Veldhuis, so the new part is applying that machinery to the Weyl group rather than to supersymmetry alone. The text has many typos and some steps are announced without full derivation, especially the Weyl gauge field action, but the overall structure of the computation is recognizable and the final actions have the expected form.
Extended reading notes
Core claim
The paper claims to derive a Weyl scale invariant p=2 brane action, Eq. (27), I = -T ∫ d^3x sqrt(|ρ|) (1/3 ρ^{mn} η_{μν} ∂_m X^μ ∂_n X^ν)^{3/2}, and a dual D2 brane Born-Infeld action, Eq. (43), from the nonlinear realization of the super-Weyl group broken to W(1,2), including localized matter actions with a Weyl gauge field.
Load-bearing premise
The inverse Higgs condition ω^Z = 0 in Eq. (19) is used to eliminate the Goldstone fields u^m, solving u^b tanh(sqrt(u^2))/sqrt(u^2) = -D^b Φ. The subsequent dreibein, metric, and actions depend on this inversion, but the paper neither proves the solution is unique nor checks for singularities in the limit where (DΦ)^2 approaches 1. If this elimination fails for some field configurations, the central action (27) would not describe the full coset manifold.
Original abstract
The action of Weyl scale invariant p=2 brane which breaks the target super Weyl scale symmetry in the N=1, D=4 superspace down to the lower dimensional Weyl symmetry W(1,2) is derived by the approach of nonlinear realization. The dual form action for the Weyl scale invariant supersymmetric D2 brane is also constructed. The interactions of localized matter fields on the brane with the Nambu-Goldstone fields associated with the breaking of the symmetries in the superspace and one spatial translation directions are obtained through the Cartan one-forms of the Coset structures. The covariant derivatives for the localized matter fields are also obtained by introducing Weyl gauge field as the compensating field corresponding to the local scale transformation on the brane world volume.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The action of Weyl scale invariant p=2 brane which breaks the target super Weyl scale symmetry in the N=1, D=4 superspace down to the lower dimensional Weyl symmetry W(1,2) is derived by the approach of nonlinear realization. The dual form action for the Weyl scale invariant supersymmetric D2 brane is also constructed. The interactions of localized matter fields on the brane with the Nambu-Goldstone fields associated with the breaking of the symmetries in the superspace and one spatial translation directions are obtained through the Cartan one-forms of the Coset structures. The covariant derivatives for the localized matter fields are also obtained by introducing Weyl gauge field as the compensating field corresponding to the local scale transformation on the brane world volume.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The action of Weyl scale invariant p=2 brane which breaks the target super Weyl scale symmetry in the N=1, D=4 superspace down to the lower dimensional Weyl symmetry W(1,2) is derived by the approach of nonlinear realization. | contribution 0.88 | 0.92 | 0.50 | asserted 1.00 |
| s1 | The dual form action for the Weyl scale invariant supersymmetric D2 brane is also constructed. | contribution 0.72 | 0.92 | 0.12 | asserted 1.00 |
| s2 | The interactions of localized matter fields on the brane with the Nambu-Goldstone fields associated with the breaking of the symmetries in the superspace and one spatial translation directions are obtained through the Cartan one-forms of the Coset structures. | result 0.50 | 0.91 | 0.17 | asserted 1.00 |
| s3 | The covariant derivatives for the localized matter fields are also obtained by introducing Weyl gauge field as the compensating field corresponding to the local scale transformation on the brane world volume. | contribution 0.47 | 0.91 | 0.11 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
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- references and citing sentences
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Human review
References
Discussion
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