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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, Maxim; Soibelman, Yan (2008). "Stability structures, motivic Donaldson-Thomas invariants and cluster transformations". arXiv: 0811.2435 [math.AG].
• Kontsevich, Maxim; Soibelman, Yan (2009). "Motivic Donaldson-Thomas invariants: Summary of results". arXiv: 0910.4315 [math.AG].
• Joyce, Dominic; Song, Yinan (2008). "A theory of generalized Donaldson-Thomas invariants". arXiv: 0810.5645 [math.AG].
• Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew (2010). "Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory". Communications in Mathematical Physics. 299 (1): 163–224. arXiv: 0807.4723 . Bibcode:2010CMaPh.299..163G. doi:10.1007/s00220-010-1071-2.
• Aganagic, Mina; Ooguri, Hirosi; Vafa, Cumrun; Yamazaki, Masahito (2011). "Wall Crossing and M-Theory". Publications of the Research Institute for Mathematical Sciences. 47 (2): 569–584. arXiv: 0908.1194 . doi:10.2977/PRIMS/44.
• Kontsevich, Maxim; Soibelman, Yan (2013). "Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry". arXiv: 1303.3253 [math.AG].

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