Exact N=2 Landau-Ginzburg Flows

TL;DR

This paper constructs exactly solvable N=2 supersymmetric flows connecting UV theories to N=2 minimal models in the IR, providing explicit S-matrices, c-functions, and exploring their properties and related models.

Contribution

It introduces new exactly solvable N=2 Landau-Ginzburg flows, determines their S-matrices and c-functions, and explores their IR fixed points and related integrable models.

Findings

The c-function runs from 3 in the UV to minimal model values in the IR.

Identification of the flows with Landau-Ginzburg models with superpotential X^{k+2}.

Discovery of integrable models with spontaneously broken supersymmetry and (0,2) supersymmetry.

Abstract

We find exactly solvable N=2-supersymmetric flows whose infrared fixed points are the N=2 minimal models. The exact S-matrices and the Casimir energy (a c-function) are determined along the entire renormalization group trajectory. The c-function runs from c=3 (asymptotically) in the UV to the N=2 minimal model values of the central charge in the IR, leading us to interpret these theories as the Landau-Ginzburg models with superpotential $X^{k+2}$. Consideration of the elliptic genus gives further support for this interpretation. We also find an integrable model in this hierarchy which has spontaneously-broken supersymmetry and superpotential $X$, and a series of integrable models with (0,2) supersymmetry. The flows exhibit interesting behavior in the UV, including a relation to the N=2 super sine-Gordon model. We speculate about the relation between the kinetic term and the cigar target-space metric.