Holographic Weyl anomaly in 8D from general higher curvature gravity

We calculate the holographic central charges for general higher curvature gravity theory dual to eight dimensional conformal field theory (CFT). To do this, we first elaborate the general form of Weyl anomaly in 8D CFT and find 11 nontrivial linearly independent curvature combinations, one of which is Euler density and the rest are Weyl invariants, including 7 nondifferentiated ones and 3 differentiated ones. The Weyl invariants are constructed as invariant polynomials of curvature tensor and covariant derivatives. We denote <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>W</a:mi><a:mrow><a:mo stretchy="false">(</a:mo><a:mi>n</a:mi><a:mo stretchy="false">)</a:mo></a:mrow></a:msub></a:math> as the Weyl invariant that contains a polynormial term with a minimum of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>n</e:mi></e:math> curvature tensors. Interestingly, since there are a total of 12 Weyl invariants in 8D, our finding means two of them are trivial and expressible as total derivatives. The resulting central charges are expressed in terms of 15 theory-dependent constants. Remarkably, we find that the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>W</g:mi><g:mrow><g:mo stretchy="false">(</g:mo><g:mn>2</g:mn><g:mo stretchy="false">)</g:mo></g:mrow></g:msub></g:math> invariant corresponds to the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>c</k:mi></k:math>-charge that is proportional to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>C</m:mi><m:mi>T</m:mi></m:msub></m:math>, while the two <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>W</o:mi><o:mrow><o:mo stretchy="false">(</o:mo><o:mn>3</o:mn><o:mo stretchy="false">)</o:mo></o:mrow></o:msub></o:math>’s are related to three-point function parameters of energy-momentum tensor. This suggests a possible connection between the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>c</s:mi></s:math>-charges of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>W</u:mi><u:mrow><u:mo stretchy="false">(</u:mo><u:mi>n</u:mi><u:mo stretchy="false">)</u:mo></u:mrow></u:msub></u:math>’s and the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>n</y:mi></y:math>-point functions of energy-momentum tensor.