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Random Geometry, Quantum Gravity and the K\"ahler Potential
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We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a background-independent measure on the space of metrics can be easily constructed from first principles. Our framework suggests the relevance of a new gravitational effective action and we show that it occurs when coupling the massive scalar field to two-dimensional gravity. This yields new types of quantum gravity models generalizing the standard Liouville case.
Forward citations
Cited by 2 Pith papers
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Quantum Liouville Cosmology
Timelike Liouville disk path integrals in fixed K-representation produce Hartle-Hawking-like states, a conjecture for all-loop wavefunctions, and a K-independent inner product for 2D quantum cosmology.
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Normalized divisor volumes in toric Calabi-Yau threefolds appear universal, and a GOE level-spacing model with a fitted mean reproduces axion statistics across the Kreuzer-Skarke axiverse.
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