higher geometry / derived geometry
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The flop transition is a continuous path in a space of noncommutative 2-geometries that starts at an ordinary complex 3-dimensional Calabi-Yau space, then passes through a point that does not correspond to an ordinary geometry (the Gepner point) and emerges afterwards again as an ordinary CY-geometry – but now with different topology.
This was found and discussed in the context of string theory but the phenomenon is a general abstract one in the theory of 2d SCFTs regarded as generalized geometries – as described at 2-spectral triple.
graphics grabbed from Greene 00
A survey is in
A rough and brief survey of the flop transition and related phenomena with many pointers to original literature is also given in
See also
On the quantum volume? of vanishing cycles in the flop transition:
Brian Greene, Yakov Kanter, Small Volumes in Compactified String Theory, Nucl.Phys.B497:127-145,1997 (arXiv:hep-th/9612181)
Brian Greene, Calin Lazaroiu, Collapsing D-Branes in Calabi-Yau Moduli Space: I, Nucl.Phys. B604 (2001) 181-255 (arXiv:hep-th/0001025)
Calin Lazaroiu, Collapsing D-branes in one-parameter models and small/large radius duality, Nucl.Phys. B605 (2001) 159-191 (arXiv:hep-th/0002004)
Mark Raugas, D-Branes and Vanishing Cycles in Higher Dimensions (arXiv:hep-th/0102133)
Last revised on January 12, 2019 at 18:01:57. See the history of this page for a list of all contributions to it.