TY  - JOUR
AU  - Aguilar, A. C.
AU  - Ferreira, M. N.
AU  - Ibañez, D.
AU  - Oliveira, B. M.
AU  - Papavassiliou, J.
PY  - 2023
DA  - 2023//
TI  - Patterns of gauge symmetry in the background field method
T2  - Eur. Phys. J. C
JO  - European Physical Journal C
SP  - 86 - 20pp
VL  - 83
IS  - 1
PB  - Springer
AB  - 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.
SN  - 1434-6044
UR  - https://arxiv.org/abs/2211.16102
UR  - https://doi.org/10.1140/epjc/s10052-023-11219-1
DO  - 10.1140/epjc/s10052-023-11219-1
LA  - English
N1  - WOS:000923274000003
ID  - Aguilar_etal2023
ER  -