BPS and non-BPS states in a supersymmetric Landau-Ginzburg theory

TL;DR

This paper investigates the BPS and non-BPS spectra of a specific supersymmetric Landau-Ginzburg model, revealing the full spectrum through UV-IR analysis and Picard-Lefschetz theory, and highlighting the impact of integrability on state scattering.

Contribution

It provides the complete BPS spectrum for a supersymmetric Landau-Ginzburg theory with a specific superpotential, using advanced mathematical techniques and considering integrability effects.

Findings

Full BPS spectrum determined via UV-IR connection

Non-BPS state masses fixed by integrability constraints

Application of Picard-Lefschetz theory to boundary singularities

Abstract

We analyze the spectrum of the N=(2,2) supersymmetric Landau-Ginzburg theory in two dimensions with superpotential W=X^{n+2}-lambda X^2. We find the full BPS spectrum of this theory by exploiting the direct connection between the UV and IR limits of the theory. The computation utilizes results from the Picard-Lefschetz theory of singularities and its extension to boundary singularities. The additional fact that this theory is integrable requires that the BPS states do not close under scattering. This observation fixes the masses of non-BPS states as well.