Quantum foam and topological strings
By Amer Iqbal, C. Vafa, N. Nekrasov, A. Okounkov. 2003
261 citations recorded by the source corpus.
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 Kahler 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 ~ gsα'.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7436f80cd6843e83bdac13e5cf9fb1d8faa9dedd
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Citations in the corpus
- D-brane Deconstructions in IIB Orientifolds (2008, background): “Ideal sheaves of a given charges are counted by (rank 1) Donaldson-Thomas invariants, which are related to Gromov-Witten invariants and hence to the topological string [121, 122, 123, 124].”
- The String Landscape, the Swampland, and the Missing Corner (2017, methodology): “We will proceed by computing the example of C3 since the techniques used generalize to other CY 3-folds [33].”
- Euclidean Wormholes, Baby Universes, and Their Impact on Particle Physics and Cosmology (2018, background): “An interesting and closely related topic, which lies beyond the scope of this work, are topological fluctuations of spacetime at small scales (the Planck scale [2, 4] or string scale [72]) as constituents of a microscopic description of quantum gravity.”
- Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions (2007, methodology): “W g(d)ed·t. We can now use the fact that Z qu has a dual interpretation as the Donaldson-Thomas partition function counting D0-D2-D6 bound states (we ignore here a subtlety with the degree zero maps) [20, 23, 46, 47, 52] Z qu(t,λ) = X n,d DT(n,d)e−nλed·t. (3.13) In this sum n∈ H 0(X,eZ) ∼= Z and d∈ ”
- Bubbling supertubes and foaming black holes (2005, methodology): “This proposal has similar features to the foam described in [48], but in [48] the foam was restricted to the compactification space, whereas here the foam naturally lives in the macroscopic spacetime and defines the interior structure of a black hole.”
- Refined, Motivic, and Quantum (2009, background): “Of course, the quantity w∞(Θ ) must be the Donaldson-Thomas partition function of the conifold, and this relation holds because pyramid partitions of length n→∞ effectively reduce to the topological vertex formalism of [12,13] (see also [27,28]).”
- Non-commutative Donaldson-Thomas theory and the conifold (2007, background): “certain subsets of the arrangement of Figure 7; note that the shape of the latter is closely related to the toric combinatorics of the resolved conifold X (indicated by the dashed line). Consequently [22, 16, 21], one obtains Theorem 2.8.1. (4) ZX(q,t) = M(−q)2 Y k≥1 1−(−q)ke−t k . In fact, the sin”
- Split states, entropy enigmas, holes and halos (2007, background): “Finally, Ztop is conjecturally related [35, 36, 37, 29] to the Donaldson-Thomas partition function for ideal sheaves, as”
- Gromov–Witten theory and Donaldson–Thomas theory, I (2003, unknown): “Introduction”
- Supergravity microstates for BPS black holes and black rings (2005, background): “’s geometric transitions picture [32, 33] and melting crystal space-time foam picture [35, 36] which will certainly attract future attention.”