Quantum foam and topological strings. (English) Zbl 1246.81338
Summary: We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral involving fluctuations of Kähler geometry and topology. We show how the limit shape of the melting crystal emerges as the average geometry and topology of the quantum foam at the string scale. The geometry is classical at large length scales, modified to a smooth limit shape dictated by mirror geometry at string scale and is a quantum foam at area scales \(\sim g_{s}\alpha '\).
MSC:
81T45 | Topological field theories in quantum mechanics |
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
81T60 | Supersymmetric field theories in quantum mechanics |
14J81 | Relationships between surfaces, higher-dimensional varieties, and physics |
14J30 | \(3\)-folds |
References:
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