Year: 2025
Type: article
Abstract: We show that the long-standing problem of gauge dependence of the effective potential arises due to the factorization of the determinant of operators, which is invalid when we take the zeta-regularized trace of the operators. We show by correcting for this assumption by computing the multiplicative anomaly, the gauge-dependent terms of the effective potential cancel. We also show that in two- and odd-dimensional noncompact spacetime manifolds where the multiplicative anomaly term is zero, the standard calculation of one-loop effective potential gives a gauge-independent result. These results are in support of our claim that the multiplicative anomaly may play a crucial role in removing the gauge dependence in the effective potential in the four-dimensional noncompact manifold. Noting the nontrivial aspects of this anomaly computation for a generic scenario, we propose the heat-kernel method to compute the effective potential where this anomaly emerges as a total derivative, thus redundant. We explicitly show how one can calculate the gauge independent, effective action and the Coleman-Weinberg effective potential by employing the heat-kernel method. Based on this result, we advocate the heat-kernel expansion as the most straightforward method, as it naturally deals with the matrix elliptic operator for the calculation of manifestly gauge independent, effective actions compared to other conventional methods.
Institution: Indian Institute of Technology Kanpur
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4409919931