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Journal of High Energy Physics

, 2011:106 | Cite as

Kähler-Einstein metrics emerging from free fermions and statistical mechanics

  • Robert J. Berman
Article

Abstract

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.

Keywords

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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