Equivalence of Three Wall Crossing Formulae

Details Equivalence of Three Wall Crossing Formulae Equivalence of Three Wall Crossing Formulae

2011-12-12

arxiv.org/abs/1112.2515v2

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 45 pages; v2: added eq.(2.10) containing explicit wall crossing formula for numerical invariants and comments on i

Scientific paper

The wall crossing formula of Kontsevich and Soibelman gives an implicit relation between the BPS indices on two sides of the wall of marginal stability by equating two symplectomorphisms constructed from the indices on two sides of the wall. The wall crossing formulae of Manschot, Pioline and the author give two apparently different explicit expressions for the BPS index on one side of the wall in terms of the BPS indices on the other side. We prove the equivalence of all the three formulae.

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