Central Charge Anomalies in 2D Sigma Models with Twisted Mass

TL;DR

This paper investigates quantum anomalies in the central charge of 2D supersymmetric sigma models with twisted masses, revealing new bosonic anomaly contributions and their supermultiplet structure, impacting BPS soliton stability.

Contribution

It provides the first direct calculation of the bosonic part of the central charge anomaly and constructs its supermultiplet with a superfield description.

Findings

Derived the bosonic part of the central charge anomaly.

Constructed the supermultiplet of all anomalies.

Presented the explicit curve of marginal stability for BPS solitons.

Abstract

We discuss the central charge in supersymmetric ${\cal N}=2$ sigma models in two dimensions. The target space is a symmetric K\"ahler manifold, CP$(N-1)$ is an example. The U(1) isometries allow one to introduce twisted masses in the model. At the classical level the central charge contains Noether charges of the U(1) isometries and a topological charge which is an integral of a total derivative of the Killing potentials. At the quantum level the topological part of the central charge acquires anomalous terms. A bifermion term was found previously, using supersymmetry which relates it to the superconformal anomaly. We present a direct calculation of this term using a number of regularizations. We derive, for the first time, the bosonic part in the central charge anomaly. We construct the supermultiplet of all anomalies and present its superfield description. We also discuss a related issue of BPS solitons in the CP(1) model and present an explicit form for the curve of marginal stability.