AdS/CFT 与 Carroll 全息中的自旋-1 体态局域态
Spin-1 Bulk Local States in AdS/CFT and Carrollian Holography
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中文总结 AI 辅助
在AdS/CFT与Carroll全息中构造有质量自旋-1体态局域态，分为两个螺旋度分支，分别对应Proca场与Maxwell-Chern-Simons理论，并通过平坦极限联系两种描述。
中文摘要 AI 辅助
我们在 AdS$_3$/CFT$_2$ 与三维 Carroll 全息中构造了有质量自旋-1 场的体态局域态。在 AdS 中，由保持体点不变的等距群协变性决定了该点处矢量的三个分量，并将解分为两个具有确定螺旋度的分支，其内积重现了 AdS$_3$ 的有质量矢量两点函数。通过将 HKLL 表示中的有质量矢量展开为边界后裔，可以逐项重现这三个分量态。这两个分支共同描述了宇称不变的 Proca 场，而单独一个分支则描述了 Maxwell–Chern–Simons 理论的单一传播模式。在 Carroll 理论的诱导表示中求解相同的条件，解同样分为两个分支。在生成元的平坦极限下，最高权模变为诱导模，AdS 态与格林函数变为其 Carroll 对应物，这支持了诱导表示作为 Carroll 全息中有质量体激发之归宿的观点。这是第一个构建的带自旋的体态局域态，从态本身到体-体传播子，再到联系两种描述的极限，均完整给出。
英文摘要
We construct the bulk local states of a massive spin-1 field in AdS$_3$/CFT$_2$ and three-dimensional Carrollian holography. In AdS, covariance under the isometries that leave a bulk point invariant determines the three components of the vector there and splits the solution into two branches of definite helicity, whose inner products reproduce the massive vector two-point function of AdS$_3$. By expanding the massive vector HKLL representation in boundary descendants, one can reproduce the three component states term by term. The two branches together describe the parity-invariant Proca field, and one alone the single propagating mode of Maxwell--Chern--Simons theory. The same conditions are solved in the induced representation of the Carrollian theory, where the solution again splits into two branches. Under the flat limit of the generators the highest weight module becomes the induced module, and the AdS states and Green's functions become their Carrollian counterparts, which supports the induced representation as the home of massive bulk excitations in Carrollian holography. This is the first bulk local state built with spin, complete from the state itself to its bulk-to-bulk propagator and to the limit relating the two descriptions.
发表机构
- University of Waterloo（滑铁卢大学）
- Kyoto University（京都大学）
- Hetao Institute of Mathematics and Interdisciplinary Sciences（河套数学与交叉科学研究院）
- Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
- University of Tokyo（东京大学）
- RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心（iTHEMS））
- Perimeter Institute for Theoretical Physics（理论物理珀塞尔研究所）
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