Polyakov形式中类Kaluza–Klein零约化的$\boldsymbol{\text{D}_p}$-膜的$\boldsymbol{\text{O}(F^2)}$ Carroll极限
Carroll Limit of $\mathcal{O}(F^2)$ $\text{D}_p$-branes from Kaluza--Klein-like Null reduction in the Polyakov Formulation
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中文总结 AI 辅助
本文通过Polyakov-KK途径构造$\text{O}(F^2)$截断$\text{D}_p$-膜的电、磁Carroll极限，揭示其与无$\text{U}(1)$ ILST弦的差异，分析自由度及与无张力/零弦的关联。
中文摘要 AI 辅助
我们通过Polyakov-KK途径构造了$\boldsymbol{\text{O}(F^2)}$截断$\boldsymbol{\text{D}_p}$-膜的电Carroll极限和磁Carroll极限，该途径结合了固定光锥动量下的单模类Kaluza–Klein约化与保留辅助世界体积框架的Dirac分类。与无$\text{U}(1)$的ILST弦不同，对于$p\boldsymbol{\text{≥}2}$，Carrollian $\text{D}_p$-膜在Dirac分类后不能被视为一致的固定框架约束系统。在电族中，该阻碍直接由世界体积$\text{U}(1)$物质部分产生；而在磁族中，框架保留是由标量动能的密度权重结构而非$\text{U}(1)$电流强制的。因此，框架必须在分类过程中保留，之后通过Dirac括号消除，预先冻结框架并非Dirac过程中的合法步骤。嵌入标量部分在ILST动能密度层级继承了Carroll–Weyl $\boldsymbol{\text{χ}}$结构，该结构是$\text{χ}$不变的，而完整标量作用量仅为$\text{χ}$协变的。$\text{χ}$向完整物质部分的局域扩展因$\text{U}(1)$部分通过Gauss、圆和$\boldsymbol{A_-}$梯度括号而受阻。电族将全局重标度保留为弱对称性，而磁族甚至对全局参数也不满足。对于$\boldsymbol{P_-≠0}$，电族和磁族分别有$\boldsymbol{d-2}$和$\boldsymbol{d-3}$个自由度，在$\boldsymbol{P_-=0}$时恢复的局域圆会进一步消除每个族中的一个自由度。这些特征表明，所得理论是与零弦及母$\text{O}(F^2)$ DBI理论不同的约束系统，我们还讨论了它们的壳上解释及与无张力/零弦的关系。
英文摘要
We construct the electric and magnetic Carroll limits of the $\mathcal{O}(F^2)$-truncated $\text{D}_p$-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 $p\geq2$ 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 $χ$ structure at the level of the ILST kinetic density, which is $χ$-invariant, whereas the full scalar action is only $χ$-covariant. The local extension of $χ$ 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 $P_{-}\neq0$ the electric and magnetic families have $d-2$ and $d-3$ degrees of freedom, and the restored local circle at $P_{-}=0$ 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 $\mathcal{O}(F^2)$ DBI theory, and we also discuss their on-shell interpretation and relation to tensionless/null strings.
