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Gravitational contributions to gauge Green’s functions and asymptotic free power-law running of gauge coupling

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Abstract

We perform an explicit one-loop calculation for the gravitational contributions to the two-, three- and four-point gauge Green’s functions with paying attention to the quadratic divergences. It is shown for the first time in the diagrammatic calculation that the Slavnov-Taylor identities are preserved even if the quantum graviton effects are included at one-loop level, such a conclusion is independent of the choice of regularization schemes. We also present a regularization scheme independent calculation based on the gauge condition independent background field framework of Vilkovisky-DeWitt’s effective action with focusing on both the quadratic divergence and quartic divergence that is not discussed before. With the harmonic gauge condition, the results computed by using the traditional background field method can consistently be recovered from the Vilkovisky-DeWitt’s effective action approach by simply taking a limiting case, and are found to be the same as the ones yielded by the diagrammatic calculation. As a consequence, in all the calculations, the symmetry-preserving and divergent-behavior-preserving loop regularization method can consistently lead to a nontrivial gravitational contribution to the gauge coupling constant with an asymptotic free power-law running at one loop near the Planck scale.

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Authors and Affiliations

  1. Kavli Institute for Theoretical Physics China (KITPC), State Key Laboratory of Theoretical Physics (SKLTP), Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Yong Tang & Yue-Liang Wu

  2. Physics Division, National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu, Taiwan

    Yong Tang

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  1. Yong Tang
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  2. Yue-Liang Wu
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Correspondence to Yong Tang.

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ArXiv ePrint: 1109.4001

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Tang, Y., Wu, YL. Gravitational contributions to gauge Green’s functions and asymptotic free power-law running of gauge coupling. J. High Energ. Phys. 2011, 73 (2011). https://doi.org/10.1007/JHEP11(2011)073

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  • DOI: https://doi.org/10.1007/JHEP11(2011)073

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