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Carroll Limit of π’ͺ(F2) Dp-branes from Kaluza--Klein-like Null reduction in the Polyakov Formulation

  • Limin Zeng
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Abstract

We construct the electric and magnetic Carroll limits of the π’ͺ(F2)-truncated Dp-brane via the Polyakov--KK route, which combines a single-mode Kaluza--Klein-like reduction at fixed light-cone momentum with a Dirac classification that keeps the auxiliary worldvolume frame. Unlike the U(1)-free ILST string, for pβ‰₯2 the Carrollian Dp-brane cannot be treated as a consistent fixed-frame constrained system after the Dirac classification. In the electric family the obstruction is directly produced by the worldvolume U(1) matter sector, while in the magnetic family the frame retention is forced by the scalar kinetic's density-weight structure rather than by the U(1) currents. The frame must therefore be retained through the classification and eliminated afterwards by Dirac brackets. Freezing it beforehand is not a legitimate step in the Dirac procedure. The embedding scalar sector inherits the Carroll--Weyl Ο‡ structure at the level of the ILST kinetic density, which is Ο‡-invariant, whereas the full scalar action is only Ο‡-covariant. The local extension of Ο‡ to the full matter sector is obstructed by the U(1) sector through the Gauss, circle and A--gradient brackets. The electric family keeps the global rescaling as a weak symmetry, while the magnetic family fails even for a global parameter. For Pβˆ’β‰ 0 the electric and magnetic families have dβˆ’2 and dβˆ’3 degrees of freedom, and the restored local circle at Pβˆ’=0 removes one further degree of freedom in each family. These features identify the resulting theories as constrained systems distinct from both the null string and the parent π’ͺ(F2) DBI theory, and we also discuss their on-shell interpretation and relation to tensionless/null strings.

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Cite

BibTeXRIS
BibTeX
@misc{zeng2026carroll,
  title = {{Carroll Limit of $\mathcalO(F^2)$ $\textD_p$-branes from Kaluza--Klein-like Null reduction in the Polyakov Formulation}},
  author = {Limin Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00797},
  eprint = {2609.00797},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00797},
}
RIS
TY  - UNPB
TI  - Carroll Limit of π’ͺ(F^2) D_p-branes from Kaluza--Klein-like Null reduction in the Polyakov Formulation
AU  - Limin Zeng
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00797
UR  - https://arxiv.org/abs/2609.00797
AB  - We construct the electric and magnetic Carroll limits of the π’ͺ(F^2)-truncated D_p-brane via the Polyakov--KK route, which combines a single-mode Kaluza--Klein-like reduction at fixed light-cone momentum with a Dirac classification that keeps the auxiliary worldvolume frame. Unlike the U(1)-free ILST string, for pβ‰₯2 the Carrollian D_p-brane cannot be treated as a consistent fixed-frame constrained system after the Dirac classification. In the electric family the obstruction is directly produced by the worldvolume U(1) matter sector, while in the magnetic family the frame retention is forced by the scalar kinetic's density-weight structure rather than by the U(1) currents. The frame must therefore be retained through the classification and eliminated afterwards by Dirac brackets. Freezing it beforehand is not a legitimate step in the Dirac procedure. The embedding scalar sector inherits the Carroll--Weyl Ο‡ structure at the level of the ILST kinetic density, which is Ο‡-invariant, whereas the full scalar action is only Ο‡-covariant. The local extension of Ο‡ to the full matter sector is obstructed by the U(1) sector through the Gauss, circle and A_--gradient brackets. The electric family keeps the global rescaling as a weak symmetry, while the magnetic family fails even for a global parameter. For P_βˆ’β‰ 0 the electric and magnetic families have dβˆ’2 and dβˆ’3 degrees of freedom, and the restored local circle at P_βˆ’=0 removes one further degree of freedom in each family. These features identify the resulting theories as constrained systems distinct from both the null string and the parent π’ͺ(F^2) DBI theory, and we also discuss their on-shell interpretation and relation to tensionless/null strings.
ER  -