Categorical Wall-Crossing in Landau-Ginzburg Models

Abstract

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 $\mathcal{N}=(2,2)$ models. We show that our jump formulas hold if and only if the $A_{\infty }$-categories of half-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.

80 pages, 18 figures

References in corpus (3)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Algebra of the Infrared: String Field Theoretic Structures in Massive $\mathcal{N}=(2,2)$ Field Theory In Two Dimensions
• FQHE and $t{t}^{\ast }$ geometry

Cited by in corpus (2)

• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Les Houches lectures on non-perturbative Seiberg-Witten geometry