Wall-crossing

String theory

Fundamental objects
String Brane D-brane
Perturbative theory
Bosonic Superstring Type I Type II (IIA / IIB) Heterotic (SO(32) · E₈×E₈)
Non-perturbative results
S-duality T-duality M-theory AdS/CFT correspondence
Phenomenology
Phenomenology Cosmology Landscape
Mathematics
Mirror symmetry Monstrous moonshine
Related concepts Conformal field theory Holographic principle Kaluza–Klein theory Quantum gravity Supergravity Supersymmetry Theory of everything Twistor string theory
Theorists Arkani-Hamed Banks Dijkgraaf Duff Fischler Gates Gliozzi Green Greene Gross Gubser Harvey Hořava Kaku Klebanov Kontsevich Maldacena Mandelstam Martinec Minwalla Moore Motl Nekrasov Neveu Olive Polchinski Polyakov Randall Ramond Rohm Scherk Schwarz Seiberg Sen Shenker Sơn Strominger Sundrum Susskind 't Hooft Townsend Vafa Veneziano E. Verlinde H. Verlinde Witten Yau Zaslow
History Glossary

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
Kontsevich, M. and Soibelman, Y., "Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry", arXiv:1303.3253

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