Gravity-induced photon interactions and infrared consistency in any dimensions

We compute the four-photon (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>F</a:mi><a:mn>4</a:mn></a:msup></a:math>) operators generated by loops of charged particles of spin 0, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mfrac><c:mn>1</c:mn><c:mn>2</c:mn></c:mfrac></c:math>, 1 in the presence of gravity and in any spacetime dimension <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>d</e:mi></e:math>. To this end, we expand the one-loop effective action via the heat kernel coefficients, which capture both the gravity-induced renormalization of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>F</g:mi><g:mn>4</g:mn></g:msup></g:math> operators and the low-energy Einstein-Maxwell effective field theory (EFT) produced by massive charged particles. We set positivity bounds on the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>F</i:mi><i:mn>4</i:mn></i:msup></i:math> operators using standard arguments from extremal black holes (for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>d</k:mi><k:mo>≥</k:mo><k:mn>4</k:mn></k:math>) and from infrared (IR) consistency of four-photon scattering (for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>d</m:mi><m:mo>≥</m:mo><m:mn>3</m:mn></m:math>). We find that both approaches yield nearly equivalent results, even though in the amplitudes we discard the graviton <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>t</o:mi></o:math>-channel pole and use the vanishing of the Gauss-Bonnet term at quadratic order for any <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>d</q:mi></q:math>. The positivity bounds constrain the charge-to-mass ratio of the heavy particles. If the Planckian <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>F</s:mi><s:mn>4</s:mn></s:msup></s:math> operators are sufficiently small or negative, such bounds produce a version of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>d</u:mi></u:math>-dimensional weak gravity conjecture (WGC) in most, but not all, dimensions. In the special case of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>d</w:mi><w:mo>=</w:mo><w:mn>6</w:mn></w:math>, the gravity-induced beta functions of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>F</y:mi><y:mn>4</y:mn></y:msup></y:math> operators from charged particles of any spin are positive, leading to WGC-like bounds with a logarithmic enhancement. In <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>d</ab:mi><ab:mo>=</ab:mo><ab:mn>9</ab:mn></ab:math>, 10, the WGC fails to guarantee extremal black hole decay in the infrared EFT, thereby requiring the existence of sufficiently large Planckian <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mi>F</cb:mi><cb:mn>4</cb:mn></cb:msup></cb:math> operators.