标题： 物质耦合的三维高自旋引力：无和有结果 显示英文标题

标题： Matter-coupled higher spin gravities in 3d: no- and yes-go results

摘要： 无质量的高自旋场在 $3d$中对宇宙常数的任何值都没有偏好。 3d 中所有无物质的高自旋引力等价于选择适当的规范代数的Chern-Simons理论。 出于各种原因，包括全息原理，将它们与物质场丰富起来非常重要。 在 $(A)dS_3$中，物质场与高自旋场的耦合在主导阶是众所周知的，并由表示理论决定。 我们将这一结果扩展到平空间，在那里相关的高自旋代数是泊松代数，即 $w_{1+\infty}$。 然而，我们证明在平空间和 $(A)dS_3$空间中都没有非平凡的高阶变形/相互作用。 尽管如此，通过用一些辅助场丰富场内容，并利用手性高自旋引力的顶点，可以在 $(A)dS_3$上构造一种奇异的物质耦合理论。 它也接受平极限。 运动方程的形式是泊松sigma模型，有意义的作用量形式是Courant sigma模型。 我们还探讨了将该理论嵌入全息对偶中的可能性。 显示英文摘要

摘要： Massless higher-spin fields show no preference for any value of the cosmological constant in $3d$. All matter-free higher-spin gravities in 3d are equivalent to Chern-Simons theories with an appropriate choice of gauge algebra. For various reasons, including holography, it is important to enrich them with matter fields. In $(A)dS_3$, the coupling of matter fields to higher-spin fields is well-known to the leading order and is determined by the representation theory. We extend this result to flat space, where the relevant higher-spin algebra is the Poisson algebra, aka $w_{1+\infty}$. However, we show that both in flat and $(A)dS_3$ spaces there are no nontrivial higher order deformations/interactions. Nevertheless, by enlarging the field content with some auxiliary fields and taking advantage of the chiral higher-spin gravity's vertices, it is possible to construct an exotic matter-coupled theory on $(A)dS_3$. It also admits a flat limit. The equations of motion have the form of a Poisson sigma-model and a meaningful action has the form of a Courant sigma-model. We also explore the potential for embedding this theory into a holographic duality.