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arXiv 1008.4579hep-thgr-qcmath-phmath.MP
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三维高自旋Anti-de Sitter引力的渐近对称性非线性W(无穷)代数

Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity

Marc Henneaux, Soo-Jong Rey

摘要:

研究了(2+1)维高自旋反de Sitter引力的渐近对称代数。我们使用的公式的理论作为一个陈-西蒙斯规范理论的基础上的高自旋代数hs(1,1)。将渐近反de Sitter时空的规范连接展开,给出了高自旋规范场的相容边界条件。然后,我们研究了剩余规范变换,相应的表面项和泊松括号代数。我们发现渐近对称代数是一个具有经典中心荷的非线性变形W(无穷)代数。我们讨论了我们的结果对量子引力和弦论中各种情况的影响。

英文摘要:

We investigate the asymptotic symmetry algebra of (2+1)-dimensional higher spin, anti-de Sitter gravity. We use the formulation of the theory as a Chern-Simons gauge theory based on the higher spin algebra hs(1,1). Expanding the gauge connection around asymptotically anti-de Sitter spacetime, we specify consistent boundary conditions on the higher spin gauge fields. We then study residual gauge transformation, the corresponding surface terms and their Poisson bracket algebra. We find that the asymptotic symmetry algebra is a nonlinearly deformed W(infinity) algebra with classical central charges. We discuss implications of our results to quantum gravity and to various situations in string theory.

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