Patterns of gauge symmetry in the background field method

A. Aguilar (Institute of Physics “Gleb Wataghin”, University of Campinas-UNICAMP, Campinas, São Paulo, 13083-859, Brazil) ; M. Ferreira (Department of Theoretical Physics and IFIC, University of Valencia and CSIC, Valencia, 46100, Spain) ; D. Ibañez (University Centre EDEM, Muelle de la Aduana, La Marina de Valencia, Valencia, 46024, Spain) ; B. Oliveira (Institute of Physics “Gleb Wataghin”, University of Campinas-UNICAMP, Campinas, São Paulo, 13083-859, Brazil) ; J. Papavassiliou (Department of Theoretical Physics and IFIC, University of Valencia and CSIC, Valencia, 46100, Spain)

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.

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      "source": "Springer", 
      "value": "The correlation functions of Yang\u2013Mills theories formulated in the background field method satisfy linear Slavnov\u2013Taylor 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\u2013Dyson equation. In the present work we demonstrate by means of explicit calculations that the same distinct realization of the Slavnov\u2013Taylor identity persists in the case of the background three-gluon vertex. The analysis is carried out at the level of the exact Schwinger\u2013Dyson 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\u2013Taylor 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."
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Published on:
28 January 2023
Publisher:
Springer
Published in:
European Physical Journal C , Volume 83 (2023)
Issue 1
Pages 1-20
DOI:
https://doi.org/10.1140/epjc/s10052-023-11219-1
arXiv:
2211.16102
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: