Kahler-Einstein metrics emerging from free fermions and statistical mechanics
Journal article, 2011

We propose a statistical mechanical derivation of Kithler-Einstein metrics, i.e. solutions to Einstein's vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kahler manifold X. The microscopic theory is given by a canonical free fermion gas on X whose one-particle states are pluricanonical holomorphic sections on X (coinciding with higher spin states in the case of a Riemann surface) defined in background free manner. A heuristic, but hopefully physically illuminating, argument for the convergence in the thermodynamical (large N) limit is given, based on a recent mathematically rigorous result about exponentially small fluctuation's of Slater determinants. Relations to higher-dimensional effective bosonization, the Yau-Tian-Donaldson program in Kahler geometry and quantum gravity are explored. The precise mathematical details will be investigated elsewhere.

Statistical Methods

Differential and Algebraic Geometry



scalar curvature




Models of Quantum Gravity


projective embeddings

Matrix Models


Robert Berman

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Journal of High Energy Physics

1126-6708 (ISSN) 1029-8479 (eISSN)

Vol. 2011 10 Art. no. 106- 106

Subject Categories

Physical Sciences



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