$\mathcal{I}$/$c$-extremization in M/F-duality

<jats:p>We study the holographic dual to <jats:inline-formula><jats:alternatives><jats:tex-math>c</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math></jats:alternatives></jats:inline-formula>-extremization for 2d <jats:inline-formula><jats:alternatives><jats:tex-math>(0,2)</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> superconformal field theories (SCFTs) that have an AdS<jats:inline-formula><jats:alternatives><jats:tex-math>_3</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi /><mml:mn>3</mml:mn></mml:msub></mml:math></jats:alternatives></jats:inline-formula> dual realized in Type IIB with varying axio-dilaton, i.e. F-theory. M/F-duality implies that such AdS<jats:inline-formula><jats:alternatives><jats:tex-math>_3</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi /><mml:mn>3</mml:mn></mml:msub></mml:math></jats:alternatives></jats:inline-formula> solutions can be mapped to AdS<jats:inline-formula><jats:alternatives><jats:tex-math>_2</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi /><mml:mn>2</mml:mn></mml:msub></mml:math></jats:alternatives></jats:inline-formula> solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic <jats:inline-formula><jats:alternatives><jats:tex-math>c</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math></jats:alternatives></jats:inline-formula>-extremization in F-theory and <jats:inline-formula><jats:alternatives><jats:tex-math>\mathcal{I}</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle mathvariant="script"><mml:mi>ℐ</mml:mi></mml:mstyle></mml:math></jats:alternatives></jats:inline-formula>-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.</jats:p>