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arXiv · 2609.21691

BMS$_3$ modules from path integrals on the coadjoint orbits

Pujian Mao·Xin-Cheng Mao
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Abstract

In this paper, we provide a systematic construction of quantum modules associated with coadjoint orbits of asymptotic symmetry groups through the path integral quantization at one-loop order. In particular, for the orbits with Hamiltonians unbounded from below, we show that an appropriate choice of integration contour defines a convergent Euclidean half-line path integral. The reference state associate with the orbit is determined by the path integral of the geometric action on the corresponding coadjoint orbit. The coadjoint module is therefore spanned by the reference state and its descendants. We apply this formalism to the Virasoro and BMS$_3$ groups and derive the coadjoint modules corresponding to all constant orbits. We also compute the characters of all constant Virasoro and BMS$_3$ coadjoint orbits by counting the states within the modules, and the results agree with the corresponding computations from the path integral of the geometric action with a periodic Euclidean direction.

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Pujian Mao, Xin-Cheng Mao. 2026-09-18. BMS$_3$ modules from path integrals on the coadjoint orbits. https://arxiv.org/abs/2609.21691

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