Journal of High Energy Physics

, 2011:106 | Cite as

Kähler-Einstein metrics emerging from free fermions and statistical mechanics

  • Robert J. Berman


We propose a statistical mechanical derivation of Kähler-Einstein metrics, i.e. solutions to Einstein’s vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kähler 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 fluctuations of Slater determinants. Relations to higher-dimensional effective bosonization, the Yau-Tian-Donaldson program in Kähler geometry and quantum gravity are explored. The precise mathematical details will be investigated elsewhere.


Models of Quantum Gravity Differential and Algebraic Geometry Statistical Methods Matrix Models 


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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesChalmers University of Technology and University of GothenburgGothenburgSweden

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