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arXiv · 2508.04220

Null infinity as $SU(2)$ Chern-Simons theories and its quantization

Hongwei Tan·Kui Xiao·Shoucheng Wang
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Abstract

This paper studies the quantization of the future null infinity ($\mathscr{I}^+$) of an asymptotically flat spacetime. Based on the observation by Ashtekar and Speziale that $\mathscr{I}^+$ can be regarded as a weakly isolated horizon, we adopt the quantization framework developed for weakly horizon to quantize $\mathscr{I}^+$. We first show that the symplectic structure of $\mathscr{I}^+$ is equivalent to the sum of the symplectic structures of two $SU(2)$ Chern-Simons theories with opposite levels. Based on this observation, we apply Chern-Simons quantization approach to quantize $\mathscr{I}^+$. Finally, we compute the entropy of $\mathscr{I}^+$ by counting the microstates, showing that it is proportional to the area of $\tilde{\Delta}$, a spacelike cross-section of $\mathscr{I}^+$. Our result is consistent with the universal entropy formula in the framework of (weakly) isolated horizon.

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Hongwei Tan, Kui Xiao, Shoucheng Wang. 2025-08-06. Null infinity as $SU(2)$ Chern-Simons theories and its quantization. https://arxiv.org/abs/2508.04220

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