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Kahler-Einstein metrics emerging from free fermions and statistical mechanics

Robert Berman (Institutionen för matematiska vetenskaper, matematik)
Journal of High Energy Physics (1126-6708). 10, p. Art. no. 106. (2011)
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Models of Quantum Gravity, Differential and Algebraic Geometry, Statistical Methods, Matrix Models, projective embeddings, scalar curvature, complex-surfaces, bosonization, manifolds, equations, spacetime, foam



Denna post skapades 2011-12-22. Senast ändrad 2015-07-02.
CPL Pubid: 150866

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Fysik

Chalmers infrastruktur