论文标题
可集成的系统和广告上较高旋转重力的边界动态$ _3 $
Integrable systems and the boundary dynamics of higher spin gravity on AdS$_3$
论文作者
论文摘要
我们引入了一组新的边界条件，用于三维更高自旋重力，并使用量规组$ sl（3，\ mathbb {r}）\ times sl（3，\ mathbb {r}）$，其中其在边界处的动力学由修改后的BousSinesq集成层的成员描述。在渐近区域中，量规场写在对角线仪表中，刺激沿着$ sl（3，\ mathbb {r}）\ oplus sl（3，\ mathbb {r}）的发电机沿着cartan subegra的发电机进行。我们表明，修改后的Boussinesq层次结构的整个可集成结构，即相位空间，泊松支架和无限的通勤保守电荷，是从高级自旋理论的渐近结构中获得的。此外，一旦在最高的重量表中重新表达了渐近条件后，其与Boussinesq层次结构的已知关系是从我们的分析中继承的。因此，Miura地图是从大体中的几何结构中回收的。还讨论了适合我们边界条件下的黑洞，边界上的哈密顿式减少以及用量规组$ sl（n，\ mathbb {r}）\ times sl（n，\ mathbb {r}）$概括较高的自旋重力。
We introduce a new set of boundary conditions for three-dimensional higher spin gravity with gauge group $SL(3,\mathbb{R})\times SL(3,\mathbb{R})$, where its dynamics at the boundary is described by the members of the modified Boussinesq integrable hierarchy. In the asymptotic region the gauge fields are written in the diagonal gauge, where the excitations go along the generators of the Cartan subalgebra of $sl(3,\mathbb{R})\oplus sl(3,\mathbb{R})$. We show that the entire integrable structure of the modified Boussinesq hierarchy, i.e., the phase space, the Poisson brackets and the infinite number of commuting conserved charges, are obtained from the asymptotic structure of the higher spin theory. Furthermore, its known relation with the Boussinesq hierarchy is inherited from our analysis once the asymptotic conditions are re-expressed in the highest weight gauge. Hence, the Miura map is recovered from a purely geometric construction in the bulk. Black holes that fit within our boundary conditions, the Hamiltonian reduction at the boundary, and the generalization to higher spin gravity with gauge group $SL(N,\mathbb{R})\times SL(N,\mathbb{R})$ are also discussed.
