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D-brane Solutions in Non-Commutative Gauge Theory on Fuzzy Sphere
High Energy Physics - Theory · Submitted 22 Jan 2001
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We identify a subset of solutions of this theory which are analogs of ``unstable'' solitons on a non-commutative flat D2-brane found by Gopakumar et al. Analogously to the flat case, these solutions have the interpretation as describing D0-branes ``not yet dissolved'' by the D2-brane.
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Non-commutative gauge theory on fuzzy sphere was obtained by Alekseev et al. as describing the low energy dynamics of a spherical D2-brane in S^3 with the background b-field. We identify a subset of solutions of this theory which are analogs of ``unstable'' solitons on a non-commutative flat D2-brane found by Gopakumar et al. Analogously to the flat case, these solutions have the interpretation as describing D0-branes ``not yet dissolved'' by the D2-brane. We confirm this interpretation by showing the precise agreement of the binding energy computed in the non-commutative and ordinary Born-Infeld descriptions. We then study stability of the solution describing a single D0-brane off a D2-brane. Similarly to the flat case, we find an instability when the D0-brane is located close to the D2-brane. We furthermore obtain the complete mass spectrum of 0-2 fluctuations, which thus gives a prediction for the low energy spectrum of the 0-2 CFT in S^3. We also discuss in detail how the instability to a formation of the fuzzy sphere modifies the usual Higgs mechanism for small separation between the branes.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Non-commutative gauge theory on fuzzy sphere was obtained by Alekseev et al. as describing the low energy dynamics of a spherical D2-brane in S^3 with the background b-field. | background 1.00 | 0.03 | 0.04 | asserted 1.00 |
| s1 | We identify a subset of solutions of this theory which are analogs of ``unstable'' solitons on a non-commutative flat D2-brane found by Gopakumar et al. Analogously to the flat case, these solutions have the interpretation as describing D0-branes ``not yet dissolved'' by the D2-brane. | contribution 0.81 | 0.91 | 0.24 | asserted 1.00 |
| s2 | We confirm this interpretation by showing the precise agreement of the binding energy computed in the non-commutative and ordinary Born-Infeld descriptions. | result 0.89 | 0.95 | 0.25 | asserted 1.00 |
| s3 | We then study stability of the solution describing a single D0-brane off a D2-brane. | contribution 1.00 | 0.87 | 0.05 | asserted 0.79 |
| s4 | Similarly to the flat case, we find an instability when the D0-brane is located close to the D2-brane. | result 1.00 | 0.95 | 0.14 | asserted 1.00 |
| s5 | We furthermore obtain the complete mass spectrum of 0-2 fluctuations, which thus gives a prediction for the low energy spectrum of the 0-2 CFT in S^3. | result 0.86 | 0.96 | 0.17 | asserted 0.93 |
| s6 | We also discuss in detail how the instability to a formation of the fuzzy sphere modifies the usual Higgs mechanism for small separation between the branes. | contribution 0.68 | 0.88 | 0.12 | asserted 0.91 |
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Original abstract
Non-commutative gauge theory on fuzzy sphere was obtained by Alekseev et al. as describing the low energy dynamics of a spherical D2-brane in S^3 with the background b-field. We identify a subset of solutions of this theory which are analogs of ``unstable'' solitons on a non-commutative flat D2-brane found by Gopakumar et al. Analogously to the flat case, these solutions have the interpretation as describing D0-branes ``not yet dissolved'' by the D2-brane. We confirm this interpretation by showing the precise agreement of the binding energy computed in the non-commutative and ordinary Born-Infeld descriptions. We then study stability of the solution describing a single D0-brane off a D2-brane. Similarly to the flat case, we find an instability when the D0-brane is located close to the D2-brane. We furthermore obtain the complete mass spectrum of 0-2 fluctuations, which thus gives a prediction for the low energy spectrum of the 0-2 CFT in S^3. We also discuss in detail how the instability to a formation of the fuzzy sphere modifies the usual Higgs mechanism for small separation between the branes.
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