The two-sphere partition function in two-dimensional quantum gravity at fixed area

Understand

We discuss two-dimensional quantum gravity coupled to conformal matter and fixed area in a semiclassical large and negative matter central charge limit.

• In this setup the gravity theory -- otherwise highly fluctuating -- admits a round two-sphere saddle.
• We discuss the two-sphere partition function up to two-loop order from the path integral perspective.
• This amounts to studying Feynman diagrams incorporating the fixed area constraint on the round two-sphere.