Anomaly Matching Conditions and the Moduli Space of Supersymmetric Gauge Theories

TL;DR

This paper studies the structure of the moduli space in N=1 supersymmetric gauge theories using algebraic geometry, proving an anomaly matching theorem that explains known results in supersymmetric QCD.

Contribution

It introduces a new algebraic geometric approach to analyze the moduli space and proves an anomaly matching theorem for supersymmetric gauge theories.

Findings

Proves an anomaly matching theorem for N=1 supersymmetric gauge theories.

Explains the connection between ultraviolet and infrared gauge invariant fields.

Provides a unified explanation for all known anomaly matching results in supersymmetric QCD.

Abstract

The structure of the moduli space of N=1 supersymmetric gauge theories is analyzed from an algebraic geometric viewpoint. The connection between the fundamental fields of the ultraviolet theory, and the gauge invariant composite fields of the infrared theory is explained in detail. The results are then used to prove an anomaly matching theorem. The theorem is used to study anomaly matching for supersymmetric QCD, and can explain all the known anomaly matching results for this case.