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We study the question of a modification of the running gauge coupling ofYang-Mills theories due to quantum gravitational effects in a compact largeextra dimensional brane world scenario with a low energy quantum gravity scale.The ADD scenario is applied for a D=d+\delta dimensional space-time in whichgravitons freely propagate, whereas the non-abelian gauge fields are confinedto a d-dimensional brane. The extra dimensions are taken to be toroidal and thetransverse fluctuation modes (branons) of the brane are taken into account. Onthis basis we have calculated the one-loop corrections due to virtualKaluza-Klein graviton and branon modes for the gluon two- and three-pointfunctions in an effective field theory treatment. Applying momentum cut-offregularization we find that for a d=4 brane the leading gravitationaldivergencies cancel irrespective of the number of extra dimensions \delta,generalizing previous results in the absence of extra-dimensions. Hence, againthe Yang-Mills \beta-function receives no gravitational corrections atone-loop. This is no longer true in a `universal' extra dimensional scenariowith a d>4 dimensional brane. Moreover, the subleading power-law gravitationaldivergencies induce higher-dimensional counterterms, which we establish in ourscheme. Interestingly, for d=4 these gravitationally induced counterterms areof the form recently considered in non-abelian Lee-Wick extensions of thestandard model -- now with a possible mass scale in the TeV range due to thepresence of large extra dimensions.

Gravitational Contributions to the Running Yang-Mills Coupling in Large Extra-Dimensional Brane Worlds