https://doi.org/10.1140/epjc/s10052-023-11219-1
Regular Article - Theoretical Physics
Patterns of gauge symmetry in the background field method
1
Institute of Physics “Gleb Wataghin”, University of Campinas-UNICAMP, 13083-859, Campinas, São Paulo, Brazil
2
Department of Theoretical Physics and IFIC, University of Valencia and CSIC, 46100, Valencia, Spain
3
University Centre EDEM, Muelle de la Aduana, La Marina de Valencia, 46024, Valencia, Spain
Received:
1
December
2022
Accepted:
8
January
2023
Published online:
28
January
2023
The correlation functions of Yang–Mills theories formulated in the background field method satisfy linear Slavnov–Taylor identities, which are naive generalizations of simple tree level relations, with no deformations originating from the ghost-sector of the theory. In recent years, a stronger version of these identities has been found to hold at the level of the background gluon self-energy, whose transversality is enforced separately for each special block of diagrams contributing to the gluon Schwinger–Dyson equation. In the present work we demonstrate by means of explicit calculations that the same distinct realization of the Slavnov–Taylor identity persists in the case of the background three-gluon vertex. The analysis is carried out at the level of the exact Schwinger–Dyson equation for this vertex, with no truncations or simplifying assumptions. The demonstration entails the contraction of individual vertex diagrams by the relevant momentum, which activates Slavnov–Taylor identities of vertices and multi-particle kernels nested inside these graphs; the final result emerges by virtue of a multitude of extensive cancellations, without the need of performing explicit integrations. In addition, we point out that background Ward identities amount to replacing derivatives of propagators by zero-momentum background-gluon insertions, in exact analogy to standard properties of Abelian gauge theories. Finally, certain potential applications of these results are briefly discussed.
© 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.