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.

arXiv comment80 pages, 18 figures

References in corpus (16)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Four-dimensional wall-crossing via three-dimensional field theory
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• D-Branes And Mirror Symmetry
• A New Supersymmetric Index
• A Bogomol`nyi equation for intersecting domain walls
• Wall-Crossing in Coupled 2d-4d Systems
• Dyons in N=4 Supersymmetric Theories and Three-Pronged Strings
• Domain Wall Junctions are 1/4-BPS States
• The Power of Holomorphy -- Exact Results in 4D SUSY Field Theories
• Wall-crossing from supersymmetric galaxies
• Algebra of the Infrared: String Field Theoretic Structures in Massive $\mathcal{N}=(2,2)$ Field Theory In Two Dimensions
• Four ways across the wall
• An Exact Solution of BPS Junctions and Its Properties
• FQHE and $t{t}^{\ast }$ geometry

Cited by in corpus (3)

• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Les Houches lectures on non-perturbative Seiberg-Witten geometry