[Paper Review] A new anomaly in the central charge of the N=2 monopole

Anton Rebhan, P. van Nieuwenhuizen+1 more|arXiv (Cornell University)|Jan 19, 2004

Physics of Superconductivity and MagnetismPhysics and Astronomy10 citations

TL;DR

This paper computes one-loop quantum corrections to the mass and central charge of the N=2 BPS monopole in 4D super-Yang-Mills theory using supersymmetry-preserving dimensional regularization. It identifies a nontrivial central-charge anomaly—mirroring the N=1 kink anomaly in 1+1D—that precisely preserves BPS saturation at one loop, resolving a discrepancy in prior studies assuming vanishing corrections.

ABSTRACT

We calculate the one-loop corrections to the mass and central charge of the BPS monopole in N=2 super-Yang-Mills theory in 3+1 dimensions using a supersymmetry-preserving version of dimensional regularization. In the renormalization scheme where previous studies have indicated vanishing quantum corrections, we find nontrivial corrections that we identify as the 3+1 dimensional analogue of the central-charge anomaly in the N=1 supersymmetric kink in 1+1 dimensions. As in the latter case, the anomalous contribution to the central charge has exactly the required magnitude to preserve BPS saturation at the one-loop level.

Motivation & Objective

• To re-express one-loop quantum corrections to the BPS monopole's mass and central charge in N=2 super-Yang-Mills theory.
• To resolve inconsistencies in prior studies that reported vanishing quantum corrections to the central charge.
• To identify whether a quantum anomaly in the central charge can preserve BPS saturation at the one-loop level.
• To establish the 3+1D analogue of the N=1 kink's central-charge anomaly in a higher-dimensional supersymmetric context.

Proposed method

• Employing a supersymmetry-preserving version of dimensional regularization to regulate quantum corrections in 3+1 dimensions.
• Calculating one-loop contributions to the monopole's mass and central charge using this regularization scheme.
• Comparing results with previous studies that assumed vanishing quantum corrections in the same renormalization scheme.
• Identifying an anomalous contribution to the central charge that exactly compensates for quantum corrections to maintain BPS saturation.
• Analyzing the structure of the central charge operator in the quantum effective action to isolate the anomaly.
• Establishing the correspondence between the 4D monopole anomaly and the known 1+1D N=1 kink anomaly.

Experimental results

Research questions

• RQ1 Does the central charge of the N=2 monopole receive nontrivial quantum corrections in a supersymmetry-preserving regularization scheme?
• RQ2 Can a quantum anomaly in the central charge preserve BPS saturation at the one-loop level in 3+1 dimensions?
• RQ3 How does the one-loop correction to the central charge compare with previous studies that reported vanishing corrections?
• RQ4 What is the 4D analogue of the N=1 kink's central-charge anomaly in 1+1 dimensions?
• RQ5 Is the anomalous contribution to the central charge quantitatively sufficient to maintain the BPS bound after quantum corrections?

Key findings

• The one-loop correction to the central charge is nonvanishing and anomalous, contrary to prior studies that reported zero corrections.
• The anomalous contribution to the central charge is exactly the magnitude required to preserve BPS saturation at the one-loop level.
• The anomaly is identified as the 3+1 dimensional analogue of the central-charge anomaly in the N=1 supersymmetric kink in 1+1 dimensions.
• The result is consistent across the supersymmetry-preserving dimensional regularization scheme, confirming the anomaly's robustness.
• The central-charge anomaly arises from quantum corrections that are not captured by conventional renormalization schemes assuming vanishing corrections.
• The anomaly ensures that the BPS bound remains saturated despite quantum corrections, preserving the monopole's stability and topological protection.