PT Journal
AU Aguilar, AC
   Ferreira, MN
   Ibañez, D
   Oliveira, BM
   Papavassiliou, J
TI Patterns of gauge symmetry in the background field method
SO European Physical Journal C
JI Eur. Phys. J. C
PY 2023
BP 86 - 20pp
VL 83
IS 1
DI 10.1140/epjc/s10052-023-11219-1
LA English
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.
ER