Abstract
Replying to J. Ellis & N. E. Mavromatos , doi:10.1038/nature10619 (2011) In a previous paper1, I used the gauge-invariant background-field method to calculate a contribution to the renormalization of electric charge due to quantum gravity that was quadratically dependent on an energy cut-off. This was done by taking a constant electromagnetic background field, F. The result was used to support the original suggestion of Robinson and Wilczek2 that quadratic divergences could lead to asymptotic freedom. This result has been criticized by Ellis and Mavromatos3 and their present submission4 gives a shortened and altered discussion of their viewpoint.
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