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

TL;DR

This paper introduces a novel time-dependent supersymmetric quantum theory in 2D N=2 theories with R-charge twisting, predicting BPS state degeneracy changes across walls of marginal stability and relating UV and IR spectra.

Contribution

It formulates a new time-dependent supersymmetric framework that connects IR wall-crossing phenomena with UV R-charge spectra using supersymmetric index invariance.

Findings

Predicts BPS degeneracy changes across walls of marginal stability

Relates UV R-charge spectrum to IR wall-crossing behavior

Provides a simpler derivation of known results via time-dependent supersymmetric quantum mechanics

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.