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arXiv · 2511.09795

Comments on the gauge dependence of the effective potential and the utility of the Vilkovisky-DeWitt formalism

Daniel W. Collison·Archil Kobakhidze
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Abstract

We provide some additional comments on the long-lived discussions surrounding an effective action and potential plagued by a number of ambiguities. We reinforce the importance of an extra condition on the gauge-fixing function, namely the vanishing of its vacuum expectation value in the absence of external sources, when concluding gauge-independence of the effective action and potential at an extremum. We advocate for the alternative construction of the effective action and potential based on the Vilkovisky-DeWitt approach, and demonstrate its independence from the gauge-fixing parameter. We also exhibit a high-temperature generalisation of this alternative construction in the specific case of the Abelian-Higgs model.

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Daniel W. Collison, Archil Kobakhidze. 2025-11-12. Comments on the gauge dependence of the effective potential and the utility of the Vilkovisky-DeWitt formalism. https://doi.org/10.1016/j.physletb.2026.140725

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