SCFTs, Holography, and Topological Strings

Understand

We show that the non-gravitational sectors of certain 6d and 5d supergravity theories can be decomposed into superconformal field theories (SCFTs) which are coupled together by pairwise identifying and gauging mutual global symmetries.

• In the case of 6d supergravity, we consider F-theory on compact elliptic Calabi-Yau 3-folds with base $B=T^4/\mathbb{Z}_n\times \mathbb{Z}_m$ and we show in many examples that the non-gravitational field theory sectors can be described as configurations of coupled 6d $(1,0)$ SCFTs.
• We also conjecture that the effective 2d $(0,4)$ SCFTs living on the self-dual strings of the 6d theories lead to holographically dual descriptions of type IIB string theory on $AdS_3\times S^3\times B$ and moreover that their elliptic genera can be used to compute the degeneracies of 5d spinning BPS black holes along with all-genus topological string amplitudes on the corresponding compact 3-fold.
• In the case of 5d supergravity, we consider M-theory on compact Calabi-Yau 3-folds and using similar ideas as in the 6d case we show the complete non-gravitational sector of 5d supergravity theories can be decomposed into coupled 5d $\mathcal{N}=1$ SCFTs.