Localization & Exact Holography

Understand

We consider the AdS_2/CFT_1 holographic correspondence near the horizon of big four-dimensional black holes preserving four supersymmetries in toroidally compactified Type-II string theory.

• The boundary partition function of CFT_1 is given by the known quantum degeneracies of these black holes.
• The bulk partition function is given by a functional integral over string fields in AdS_2.
• Using recent results on localization we reduce the infinite-dimensional functional integral to a finite number of ordinary integrals over a space of localizing instantons.