N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons

TL;DR

This paper explores N=2 supersymmetric sigma models with twisted mass and superpotential, revealing novel central charges, spontaneous supersymmetry breaking phenomena, and proposing a new index for counting short multiplets in two-dimensional theories.

Contribution

It demonstrates the emergence of unique central charges in the superalgebra and introduces an index for counting short multiplets without relying on fermion number.

Findings

Central charges appear only in two dimensions.

Spontaneous partial supersymmetry breaking occurs in the model.

A new algebraic index for short multiplets is constructed.

Abstract

We consider supersymmetric sigma models on the Kahler target spaces, with twisted mass. The Kahler spaces are assumed to have holomorphic Killing vectors. Introduction of a superpotential of a special type is known to be consistent with N=2 superalgebra (Alvarez-Gaume and Freedman). We show that the algebra acquires central charges in the anticommutators {Q_L, Q_L} and {Q_R, Q_R}. These central charges have no parallels, and they can exist only in two dimensions. The central extension of the N=2 superalgebra we found paves the way to a novel phenomenon -- spontaneous breaking of a part of supersymmetry. In the general case 1/2 of supersymmetry is spontaneously broken (the vacuum energy density is positive), while the remaining 1/2 is realized linearly. In the model at hand the standard fermion number is not defined, so that the Witten index as well as the Cecotti-Fendley-Intriligator-Vafa index are useless. We show how to construct an index for counting short multiplets in internal algebraic terms which is well-defined in spite of the absence of the standard fermion number. Finally, we outline derivation of the quantum anomaly in {\bar Q_L, Q_R}.