2d Wall-Crossing, R-twisting, and a Supersymmetric Index

Abstract

Starting from N=2 supersymmetric theories in 2 dimensions, we formulate a novel time-dependent supersymmetric quantum theory where the R-charge is twisted along the time. The invariance of the supersymmetric index under variations of the action for these theories leads to two predictions: In the IR limit it predicts how the degeneracy of BPS states change as we cross the walls of marginal stability. On the other hand, its equivalence with the UV limit relates this to the spectrum of the U(1) R-charges of the Ramond ground states at the conformal point. This leads to a conceptually simple derivation of results previously derived using tt* geometry, now based on time-dependent supersymmetric quantum mechanics.

28 pages

References in corpus (6)

• 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
• BPS Wall Crossing and Topological Strings

Cited by in corpus (11)

• R-Twisting and 4d/2d Correspondences
• Spectral networks
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• BPS Degeneracies and Superconformal Index in Diverse Dimensions
• TASI lectures on complex structures
• More Arnold's N = 2 superconformal gauge theories
• On a hyperholomorphic line bundle over the Coulomb branch
• Superconformal Index, BPS Monodromy and Chiral Algebras
• FQHE and $t{t}^{\ast }$ geometry
• Four-dimensional N=2 Field Theory and Physical Mathematics
• A Remark on Supersymmetric Bubbles and Spectrum Crossover