2D Quantum Gravity on Compact Riemann Surfaces and Two-Loop Partition Function: Circumventing the c=1 Barrier?

Understand

We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kaehler formalism where the basic quantum field is the (Laplacian of the) Kaehler potential.

• We do a careful first-principles computation of the fixed-area partition function $Z[A]$ up to and including all two-loop contributions.
• This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices.
• Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur.