Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-02-18
Acta Physica Polonica B Proceedings Supplement vol. 4 (2011) page 461
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, 5 figures; Contribution to the proceedings of "Geometry and Physics in Cracow", Jagiellonian University, Cracow, Pol
Scientific paper
10.5506/APhysPolBSupp.4.461
We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological string theory and quantum gravity. Its partition function can be computed by enumerating the contributions from noncommutative instantons to a six-dimensional cohomological gauge theory, which yields a dynamical realization of the crystal as a discretization of spacetime at the Planck scale. We describe analogous relations between a melting crystal model in two dimensions and N=4 supersymmetric Yang-Mills theory in four dimensions. We elaborate on some mathematical details of the construction of the quantum geometry which combines methods from toric geometry, isospectral deformation theory and noncommutative geometry in braided monoidal categories. In particular, we relate the construction of noncommutative instantons to deformed ADHM data, torsion-free modules and a noncommutative twistor correspondence.
No associations
LandOfFree
Crystals, instantons and quantum toric geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Crystals, instantons and quantum toric geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Crystals, instantons and quantum toric geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-213162