Categorical wall-crossing in Landau–Ginzburg models

We describe how categorical BPS data including chain complexes of solitons, CPT pairings, and interior amplitudes jump across a wall of marginal stability in two-dimensional N = (2, 2) models.We show that our jump formulas hold if and only if the A ∞ -categories of 1 2 -BPS branes constructed on either side of the wall are homotopy equivalent.These results can be viewed as categorical enhancements of the Cecotti-Vafa wall-crossing formula.and the BPS index would be the "new index" Tr Rij F (-1) F of [CFIV].The spectrum of F on R ij lies in a Z-torsor, so after a suitable phase redefinition, the μ ij will be integers.