https://doi.org/10.1140/epjc/s10052-023-11553-4
Regular Article - Theoretical Physics
Gradient-flowed order parameter for spontaneous gauge symmetry breaking
1
RIKEN iTHEMS, Wako, 351-0198, Saitama, Japan
2
Department of Physics, Shiv Nadar Institution of Eminence, 201314, Gautam Buddha Nagar, India
3
Department of Mathematics, Tokyo Woman’s Christian University, 167-8585, Tokyo, Japan
Received:
30
March
2023
Accepted:
22
April
2023
Published online:
2
June
2023
The gauge-invariant two-point function of the Higgs field at the same spacetime point can make a natural gauge-invariant order parameter for spontaneous gauge symmetry breaking. However, this composite operator is ultraviolet divergent and is not well defined. We propose using a gradient flow to cure the divergence from putting the fields at the same spacetime point. As a first step, we compute it for the Abelian Higgs model with a positive mass squared at the one-loop order in the continuum theory using the saddle-point method to estimate the finite part. The order parameter consistently goes to zero in the infrared limit of the infinite flow time.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
