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arXiv · 2507.22318

The $\theta$-vacuum from functional renormalisation

Yuepeng Guan·Jan M. Pawlowski·Masatoshi Yamada
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Abstract

We study topological properties of a quantum mechanical system with $U(1)$-symmetry within the functional renormalisation group (fRG) approach. These properties include the vacuum energy structure and the topological susceptibility. Our approach works with a complexification of the flow equation, and specifically we embed the original symmetry into the complex plane, $U(1)\rightarrow \mathbb{C}$. We compute the effective potential of a given topological sector by restricting ourselves to field configurations with a given generalised non-trivial Chern-Simons numbers. The full potential is directly constructed from these sector potentials. Our results compare well with the benchmark results obtained from solving the corresponding Schr\"odinger equation.

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Yuepeng Guan, Jan M. Pawlowski, Masatoshi Yamada. 2025-07-30. The $\theta$-vacuum from functional renormalisation. https://doi.org/10.1103/pryh-22dx

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