Abstract: |
There are many extremization principles to find the exact R-symmetry of superconformal field theories. They involve extremizing trial central charges (in even dimensions) or sphere partition functions (in odd dimensions) with respect to a trial R-symmetry. They are known as a-maximization, F-maximization, c-extremization and I-extremization in four, three, two and one dimensions, respectively. Recently, a gravitational dual for c-extremization and I-extremization has been proposed in the literature for D3 brane and M2 brane theories, extending previous results valid for a- and F-maximization. In this talk, I discuss the equivalence of the QFT and gravitational constructions, uncovering interesting geometrical structures. |