Perturbative Quantum Corrections to the Supersymmetric CP^1 Kink with Twisted Mass

TL;DR

This paper calculates one-loop quantum corrections to the mass and central charges of a supersymmetric CP^1 kink with twisted mass, confirming theoretical predictions and revealing a quantum anomaly consistent with dual gauge theory results.

Contribution

It provides an explicit supersymmetry-preserving calculation of quantum corrections to a soliton in a supersymmetric model, highlighting anomaly effects and their agreement with duality-based predictions.

Findings

Mass and one central charge corrections are nontrivial but saturate the BPS bound.

The other central charge remains uncorrected.

Quantum anomaly manifests as parity violation in the regularization scheme.

Abstract

We present an explicit calculation of the one-loop quantum corrections to the mass and the two central charges of the kink solution of an N=(2,2) supersymmetric CP^1 model with twisted mass, using supersymmetry preserving dimensional regularization adapted to solitons. We find that the quantum corrections of the mass and one of the central charges are nontrivial (but saturate the BPS bound), while the other central charge receives no corrections. The nontrivial central charge correction corresponds to a quantum anomaly, which in our scheme appears as parity violation in the regulating extra dimension, and its magnitude is in agreement with exact results obtained by Dorey on the basis of a massive analog of mirror symmetry from a dual U(1) gauge theory, confirming also the recent work by Shifman, Vainshtein, and Zwicky.