%0 Journal Article
%T Patterns of gauge symmetry in the background field method
%A Aguilar, A. C.
%A Ferreira, M. N.
%A Ibañez, D.
%A Oliveira, B. M.
%A Papavassiliou, J.
%J European Physical Journal C
%D 2023
%V 83
%N 1
%I Springer
%@ 1434-6044
%G English
%F Aguilar_etal2023
%O WOS:000923274000003
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=5481), last updated on Mon, 13 Mar 2023 08:11:53 +0000
%X 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.
%R 10.1140/epjc/s10052-023-11219-1
%U https://arxiv.org/abs/2211.16102
%U https://doi.org/10.1140/epjc/s10052-023-11219-1
%P 86 - 20pp