Konishi Anomaly and Central Extension in N=1/2 Supersymmetry

TL;DR

This paper explores the structure of N=1/2 supersymmetry, revealing its central extension supported by domain walls, and analyzes the Konishi anomaly, proposing a gauge-invariant completion for the anti-holomorphic part.

Contribution

It demonstrates the existence of central extension in N=1/2 supersymmetry and provides a detailed analysis of the Konishi anomaly, including a novel gauge-invariant formulation.

Findings

Central charges supported by domain walls are computed.

Holomorphic part of the Konishi anomaly matches expected form.

Anti-holomorphic Konishi anomaly requires gauge-invariant completion.

Abstract

We show that the 4-dimensional N=1/2 supersymmetry algebra admits central extension. The central charges are supported by domain wall and the central charges are computed. We also determine the Konishi anomaly for N=1/2 supersymmetric gauge theory. Due to the new couplings in the Lagrangian, many terms appears. We show that these terms sum up to give the expected form for the holomorphic part of the Konishi anomaly. For the anti-holomorphic part, we give a simple argument that the naive generalization has to be modified. We suggest that the anti-holomorphic Konishi anomaly is given by a gauge invariant completion using open Wilson line.