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

Abstract

We perform an explicit one-loop calculation for the gravitational contributions to the two-, threeand 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.

Interacting scalar fields in the context of effective quantum gravity

“…Although different in a form, this gravitational correction leads to the same conclusions as those drawn by Robinson and Wilczek [27]. This result has been also derived by Ho et al [35] in momentum subtraction scheme and corrected by Tang and Wu [36,37] in the loop regularization scheme. The power law correction has been criticized by may authors.…”

Quadratic contributions of softly broken supersymmetry in the light of loop regularization

“…[11,12] is an ideal regularization scheme in studying both theoretical and phenomenological properties of SUSY and softly broken SUSY. LORE is believed to be able to preserve various symmetries, including Poincare symmetry, gauge symmetry, SUSY, etc, 2 and has already been applied in several studies, such as the one-loop renormalization of Non-Abelian gauge theories [13], the study of composite Higgs model [14], the gravitational corrections to the running of gauge couplings [15][16][17], the renormalization of supersymmetric field theories [18], the trace anomaly in quantum electrodynamics (QED) [19], the diphoton channel of the Higgs decay [20], the quadratic running of the effective Higgs mass parameter. In Ref.…”

Gravitational corrections to a non-Abelian gauge theory

“…Gravitational contributions on the running of gauge coupling in the Einstein-Yang-Mills theory were also calculated in Refs. [31,32], where the authors compared different regularization schemes and found that, while dimensional regularization leads to no gravitational contribution at one-loop, the use of loop regularization leads to a nonzero contribution that is proportional to µ 2 . They claim that, although the Slavnov-Taylor identities are satisfied irrespective of the regularization scheme used, the gravitational correction for beta function is scheme-dependent.…”

“…As we can see from eqs. (17a),(20a),( 22),( 24),( 26),( 29), (32), the Slavnov-Taylor identities are respected, since we have…”