We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as 'stability functions'. We introduce a new stability invariant - the critical value of the coupling constant - defined as the minimal coupling constant for which the partition function converges. It measures the minimal degree of stability of geodesic rays in the space the Bergman metrics, with respect to the action. We calculate this critical value when the action is the ν-balancing energy, and show that γkcrit = k - h on a Riemann surface of genus h.
- Differential and Algebraic Geometry
- Matrix Models
- Models of Quantum Gravity
ASJC Scopus subject areas
- Nuclear and High Energy Physics