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In algebraic geometry and string theory, the phenomenon of wall-crossing describes the discontinuous change of a certain quantity, such as an integer geometric invariant, an index or a space of BPS state, across a codimension-one wall in a space of stability conditions, a so-called wall of marginal stability.

References

Kontsevich, M. and Soibelman, Y. "Stability structures, motivic Donaldson–Thomas invariants and cluster transformations" (2008). arXiv:0811.2435.
M. Kontsevich, Y. Soibelman, "Motivic Donaldson–Thomas invariants: summary of results", arXiv:0910.4315
Joyce, D. and Song, Y. "A theory of generalized Donaldson–Thomas invariants," (2008). arXiv:0810.5645.
Gaiotto, D. and Moore, G. and Neitzke, A. "Four-dimensional wall-crossing via three-dimensional field theory" (2008). arXiv:/0807.4723.
Mina Aganagic, Hirosi Ooguri, Cumrun Vafa, Masahito Yamazaki, "Wall crossing and M-theory", arXiv:0908.1194

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