Lipstein Arthur, Nagy Silvia
Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom.
Phys Rev Lett. 2023 Aug 25;131(8):081501. doi: 10.1103/PhysRevLett.131.081501.
We show that self-dual gravity in Euclidean four-dimensional anti-de Sitter space (AdS_{4}) can be described by a scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalization of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS_{4} version of the so-called kinematic algebra. We also obtain the three-point interaction vertex of self-dual gravity in AdS_{4} from that of self-dual Yang-Mills by replacing the structure constants of the Lie group with the structure constants of the new kinematic algebra, implying that self-dual gravity in AdS_{4} can be derived from self-dual Yang-Mills in this background via a double copy. This provides a concrete starting point for defining the double copy for Einstein gravity in AdS_{4} by expanding around the self-dual sector. Moreover, we show that the new kinematic Lie algebra can be lifted to a deformed version of the w_{1+∞} algebra, which plays a prominent role in celestial holography.
我们证明，欧几里得四维反德西特空间（AdS₄）中的自对偶引力可以由一个具有三次相互作用的标量场来描述，该相互作用用变形的泊松括号表示，这为平坦空间中自对偶引力的普莱班斯基作用提供了一个非常简单的推广。这意味着自对偶引力中存在一种新的对称代数，特别是所谓运动学代数的AdS₄版本。我们还通过用新运动学代数的结构常数替换李群的结构常数，从自对偶杨-米尔斯理论的三点相互作用顶点得到了AdS₄中自对偶引力的三点相互作用顶点，这意味着AdS₄中的自对偶引力可以通过双拷贝从该背景下的自对偶杨-米尔斯理论导出。这为通过围绕自对偶部分展开来定义AdS₄中爱因斯坦引力的双拷贝提供了一个具体的起点。此外，我们表明新的运动学李代数可以提升为w₁+∞代数的变形版本，该代数在天体全息学中起着重要作用。
